How hard to push 3rd set?

No preflop raise, so only 66 and a limped AA or KK beat me. Or just in general how hard do you play 2nd set? 3rd set?

PokerStars 2/4 Hold'em (10 handed) FTR converter on zerodivide.cx

Preflop: Hero is MP2 with 8h, 8s. CO posts a blind of $2.
1 fold, UTG+1 calls, 2 folds, Hero calls, 1 fold, CO (poster) checks, Button calls, 1 fold, BB checks.

Flop: (5.50 SB) Ks, As, 8c (5 players)
BB checks, UTG+1 checks, Hero bets, CO raises, Button folds, BB folds, UTG+1 calls, Hero 3-bets, CO calls, UTG+1 calls.

Turn: (7.25 BB) 6d (3 players)
UTG+1 checks, Hero bets, CO folds, UTG+1 raises, Hero 3-bets, UTG+1 calls.

River: (13.25 BB) 6c (2 players)
UTG+1 bets, Hero raises, UTG+1 3-bets, Hero caps, UTG+1 calls.

Final Pot: 21.25 BB