1. I'm on the button. No reads on the villain, I just sat down.

Dealt to Ibanezrg [6h] [Ah]
Jentre folds
malko61 calls $0.25
Ibanezrg raises to $1.15
ayu31 folds
TONY-fran calls $0.90
malko61 folds
*** FLOP *** [As] [5s] [7s]
TONY-fran checks
Ibanezrg bets $2.70
TONY-fran calls $2.70
*** TURN *** [As] [5s] [7s] [Qd]
TONY-fran checks
Ibanezrg bets $8.10
TONY-fran calls $7.40 and is all-in
Uncalled bet of $0.70 returned to Ibanezrg
*** SHOW DOWN ***
TONY-fran shows [Th] [Ad]
Ibanezrg shows [6h] [Ah]
*** RIVER *** [As] [5s] [7s] [Qd] [Kh]

Should I have checked behind here on the turn given that all I am realistically getting called by are hands that are beating me i.e higher aces and a made flush, and then call a smallish bet on the river.

2. Also what do I do here? On the button again. Villain has quadrupled up. He runs 40/8/1.55

Dealt to Ibanezrg [Ad] [9s]
stephan1976 folds
R_Klein folds
DazO77 calls $0.25
Ibanezrg raises to $1.15
seabet folds
Tornano681 folds
DazO77 calls $0.90
*** FLOP *** [4c] [2d] [9c]
DazO77 bets $5.85
Me????

No reads on him doing this. However, at micro stakes I have seen this overbet been used by AA (though that was preflop) and I myself have used it (at the right time of course!)