Hey, TDarien -
First off, yes, anybody can be HIDDEN FROM VIEW by simply moving back behind the tree. I wouldn't consider this a Stealth check, or any check for that matter. It's a simple fact. There's now a tree between the two of you and they can't see you anymore.
But that's not what the game term of Hidden means. In game terms it's giving you an advantage to attack because of the state of being Hidden. It should probably be a Condition.
In the game, whenever you try to Hide, the opponent gets at least a Passive Perception, and quite likely an active Perception check. You can be completely hidden from view, but with a good Perception check the opponent can negate your attempt to Hide by hearing you, seeing you, seeing a shadow, tells from your allies, etc., or just deduction.
That Perception could be entirely independent of being able to see you or hear you. They've just 'figured out where you are.' As a result, you don't have advantage to your attack anymore and you are no longer Hidden (from that opponent). You can remain Hidden from others until that opponent tells them where you are. Then you are no longer Hidden from them either. Even if they can't see or hear you.
Now you could go through the trouble of another Hide/Perception check in the next round if you want to try to Hide again (to gain advantage). But I think that unless the circumstances warrant something different, their Perception check automatically succeeds. I suppose you could just give them a hefty bonus, or advantage on their Perception check, but there are certain circumstances that I think would go beyond stretching the limits of plausibility.
This goes back to the original question as to whether the halfling rogue could attempt to hide every round. Depending on your interpretation of the rules, sure you could do that. But I disagree with that interpretation of the rules, and feel that just ducking behind your ally after attacking each round doesn't make sense. Yes, you could wait until they succeeded at their Perception check, or the halfling missed an attack. But once that's occured (or somebody else points out the halfling to the target), I think that the circumstances don't warrant just trying again.
Climbing up the tree IS a change in circumstance. The fact that you're hidden from view gives you the opportunity to attempt to Hide. If they could see you when you started climbing up the tree, you wouldn't be able to Hide. You might be able to move to the backside and be hidden from view. You are correct that the Stealth check is a Hide check. And you are also correct that you don't have to move to attempt to Hide. But the opportunity to attempt to Hide (and gain advantage) is because you are moving under concealment. You are changing the circumstances. Otherwise the opponents perception is that you are where they expect you to be. And your attacking from that position without moving confirms this and thus no advantage.
In many cases when you attack while Hidden (and have advantage), you will become at least partially visible. That doesn't negate your advantage, though. Missing your attack does, even if they still can't see or hear you. You may still be able to remain hidden, just as a sniper can often get off several shots before their location is pinpointed. Once it is, unless the sniper moves, they've lost their advantage.
There are also situations where you could even be seen by your target, but still gain the advantage, such as being one in a crowd. I might use a Deception instead of a Stealth check depending on the circumstances, but the result is the same - you would have advantage on your attack due to being hidden.
As I stated before, invisibility is a different situation altogether because you're invisible, not hiding. There are different reasons as to why you maintain advantage while invisible, although it still falls under the category of not being seen.
But the point is, at least in terms of the rules, there's a difference between hiding, and Hiding (where you gain advantage to attack).
I would prefer to use the term concealed for somebody that is hidden from view (total concealment), but not Hidden (in an unknown location). There are certainly benefits to being concealed. For example, if you are firing arrows from a dark hallway into a room, after the first shot, or possibly the second, you'd no longer have advantage on your attack. They may not know exactly where you are, but the arrows are coming from the hall and they can prepare for additional attacks. According to the rules if you miss, you'd also lose the advantage of being Hidden.
On the other hand, your opponent would have a disadvantage attacking you since they can't see you and target you specifically.
Using this approach there's a distinct difference that's missing right now. One of the advantages that being concealed would definitely confer is the opportunity to hide. There are 3 doors in the dark hallway. Your opponent might even hear you open and close a door. But you're still hidden because they don't know which one.
If two of the doors are locked, and they enter (or light) the hallway and you're not there, now you're simply concealed because they know you went through the door that's unlocked. If, however, you were able to open one of the locked doors, you'd be hidden because you tricked them into thinking you were someplace you weren't.
Concealed is covered in the section of not being able to see your target, but it's not given specific terminology. I think that Behind Cover, Concealed, Hidden, and Invisible should all be Conditions with specific definitions to differentiate them from the general terms that make this more confusing.
But basically, my concern as a DM is whether you are Hidden and receive the advantage to your attack. That's what the original discussion was about, can the halfling rogue Hide behind an ally every round and gain advantage. I say no. They can conceal themselves. They can be hidden from view. But they can't gain advantage every round without some other change in the circumstance that would cause the opponent to potentially fail (require another) Perception check.
So I do think that the rules support my position, including the bolded part in your prior post. It's inferred with the way Perception, the rules as written for Hiding, etc. are presented. That doesn't mean that I think that it doesn't support your position, or other alternate interpretations. There's a lot of room for interpretation, because there are pretty much an endless number of possible scenarios.
Part of what I'm looking for is consistency. If you're Hidden, you have advantage to your attack. You can be unseen and unheard, but if you don't also have advantage to your attack, you're not Hidden. That's why I think it should be a Condition.
Hidden: You gain advantage on your attack rolls against any opponent who does not know your position. You could be in plain sight (such as on top of a wall but unnoticed), disguised in a crowd, behind cover, concealed, obscured, or otherwise undetected by your target. A successful attack may reveal your position, as will a missed attack, failed opposed Stealth/Perception or Deception/Perception check, the ability of the target to see or hear you, or somebody else revealing your position. Once your position is known, circumstances must permit you to cause the opponent to lose track of your position. Simply concealing yourself again is not normally sufficient. You must be able to convince your opponent that you are someplace other than your current location. You may also receive the benefits of being behind cover or concealed depending on the circumstances.
Concealed: You are concealed when your opponent knows where you are, but cannot see you. Opponents attack you with disadvantage when concealed. You could be shrouded in darkness, obscured by underbrush, or otherwise out of site, but your opponent knows where your current position is. This could be the result of observation, the result of a failed Hide attempt, or after your position is revealed due to an attack, or somebody revealing your position.
Yes, these would be house rules, but I see them more as clarifications of the existing rules.
Incidentally, I love these types of discussions, and I think it really does help a lot of people (including me) to clarify the scenario. Once again I will give my usual YMMV disclaimer. This works for me and my players. It makes sense to us. But you do what makes sense to you. It's also what makes this rule system so great.
Randy