Btn - $110.50 - 24/20 over 25 hands, steal 80%
SB - $202.05 - Hero - Ac8c

Preflop:
Btn raises to $3.00, SB raises to $10.00, Btn calls $7.00

Flop($19.95): Jd4h2s
SB bets $10.50, Btn calls $10.50

Turn($40.00): 3d
Hero?

Over the 36 hands I've played at the table, I 3bet the first time the previous hand vs the btn with AK. The fact that I just 3bet, does that make 3betting A8s worse the very next hand? Is there any psychological effect of the btn not wanting to fold because I just 3bet?

I have a few questions:
1) Preflop, is this a better flat than a 3bet since we can check call more effectively with a pair of 8's vs a hand like A4s
2) On the flop, should I check/fold since I don't have back door clubs to barrel? Or should I go for a double barrel to try and get 88-TT, AK, AQ to fold? Don't think firing one/giving up is a good strategy, given he's probably likely to continue on the flop a lot.