You're right, I forgot to take JJ and KK out of the second equity calculation, no wonder it looked so good.

You say he doesn't c-bet JJ or KK, then what are we hoping he checks behind on turn? correct me if I'm wrong, but that leaves AK as the only hand that doesn't have us ~99% beat? is it really worth calling flop in hopes of tieing for the pot? We're calling $3.50 to win $2.88, and folding to any further aggression.

The point I was trying to make was that on the turn, we're given no information to narrow his range from what it was PF. We're first to act so the decision becomes b/f or c/f. Obviously seeing how villain played the turn and river, we have more information than when it was our turn to act on the turn and I think that might be biasing some decisions. If OP posted this instead would b/f still be as bad?

Preflop: Hero is BB with K, A
UTG calls $0.50, 2 folds, MP2 bets $2.50, 3 folds, Hero calls $2, 1 fold

Flop: ($5.75) Q, A, Q (2 players)
Hero checks, MP2 bets $3.50, Hero calls $3.50

Turn: ($12.75) 8 (2 players)
Hero???