So here’s the thing, either you are dual-wielding, in which case you get two attacks plus parrying (and if neither of the weapons you are wielding have the parrying property, you are making a very sub-optimal choice), or you are wielding a two-handed weapon with parrying (again, unless you aren’t concerned about losing a really good benefit), or you are going sword and board and can’t use parrying.
Everything (damage, defense, action economy, free-hand availability, build resources needed (if you are using fighting styles or feats)) needs to be compared for those three configurations and they should come out roughly balanced.
My claim is essentially that parrying is too good compared to the alternative options.
With a greatsword the average weapon damage is 7, and you get an average 2.5 boost to AC once per round with no action needed (I had missed that it doesn‘t apply to ranged attacks, and that is a worthwhile consideration), and a free hand when you aren’t actually attacking.
With dual-wielding you get 8 damage, an average 2.5 boost to AC once per round with no action needed, but no easy free hand usage. You also get the best return on character build resource investment.
With sword and board you get 4.5 damage, a 3 point boost to your AC at the cost of you bonus action (or 2 points if you don’t use your bonus action on it) and no easy free hand usage.
The number of attacks a melee character can expect to take is of course highly variable. But in my experience it is not at all unusual for an individual melee character to take only one attack, at least until you get to higher levels, and also it is uncommon to be targeted by more than 2 attacks (again, until you get to higher levels). If I had to pick an “average times attacked per round“ for melee characters up through about level 5-6 (the level ranges that see more play than any others) I’d say 2x per round. So, going with that, lets just cut in half the bonus, and say its +1.25 AC per turn on average (for the sake of argument I’m disregarding the designer clarification that you can stack the parrying property or use it twice if you are dual wielding, since I think it‘s already potentially unbalanced without that).
Case 1: Damage 7; AC +1.25 melee; free hand when not attacking
Case 2: Damage 8; AC +1.25 melee; best return on further character build resources
Case 3: Damage 4.5; AC +2 (+3 with bonus action) melee or ranged; crit negation potential
The way I see this, case 1 and 2 are balanced well enough with each other, but case three is underpowered.