The thing is that even in 1st ed a +1 or +2 weapon wasn't all that special. I mean how many +1 weapons were floating around Homlett as published in 1979?
Elmo had a +1 axe, +1 Chain, +2 shield and +2 dagger.
Rannos had a +1 dagger, +1 leather, +2 Short Sword and a +1 ring of protection.
Germag had a +2 chain shirt
Mellub had a +1 dagger and a +1 sword
Black Jay had +1 arrows, a cloak and boots of elvinkind
Terjon had a +1 mace
I could go on.
+x items to me have always been quite pedestrian. They're just there. Generally speaking I've always described items with up to a +2 being simply 'superior'. It depends on the overall tone of the campaign I am trying to set but a +1 sword might merely be castle forged steel. A +2 item might be a master crafted, pattern welded blade.
In my current (Labyrinth Lord) campaign which is a mashup of sword and planet style pulp like Burroughs Mars series, Vances Demon princes and Planet of Adventure, Bashki's wizards and Heavy Metal magazine.
Weapons up to +2 are forged of "starmetal" a strange alloy, lighter, stronger and more flexible that steel that becomes mutable when specific alchemical processes are undertaken on it. The metal itself is rare, but not terribly so, some societies even use it for high value coins. A master smith likely knows the techniques for working it. The difference between +1 and +2 is really only the capability of the smith working it. The same deal works for metal armour. Leather armour is a bit tougher, my solution was to simply make better leather out of more exotic creature types. Still no magic involved, it's just rarer and more expensive due to the difficulty in collecting it.
Its only once you hit +3 weapons and armour that things start getting magical. Or, rather they start taking the form of lost technology. A +3 sword might have a small power supply in it that causes the blade to vibrate at an extremely fast rate, a +5 sword is basically a light saber or Warhammer style power weapon. Even looking at modules it's the +3 and above weapons that start getting rare, so those are the ones that I'm willing to spend the time on fancying up.
Hell, by the time PC's are at a level where I'm thinking of handing out +3 weapons I'm just as likely to start doling out ray guns, power armour and plasma weapons, not to mention flying boats, robots, command codes for ancient orbital weapon platforms and so on. Hell one of the BBEG's (that has yet to see use) basically rampages around on an OGRE.