Did I get max value?

Playing 1/2 over 200bb effective.

I look down at AhAc in the small blind.

5 limps when it gets to me, I raise to $20. Folds to a player in MP who calls. Pot is approximately $50.

Flop: Jc 3d 8h

I check out of position as I think I should be doing with my entire range against a recreational player.

Villain bets $15, I call.

Turn: Ad

I check to him again, I felt like leading on this card looks way to strong after just check calling flop.

Villain bets $20 into a pot of $80.

Again I feel like raising the turn looks way to strong and will likely shut down most of his worse value on the river. So I just call.

River: 3c

Since he has bet twice, I take kind of a gamble and check to him for a third time, luckily he bets out $25 into a pot of $120. I tank for about 15 seconds trying to decide what size to raise to and figure that I want to get called by a strong Ace (AJ-AK that didn’t 3 bet pre) and a naked 3. Not much two pair that he should have here besides what’s on the board. I decide to go 5x and check raise to $125. He tanked for like 15 seconds and then flicks in the call. I turn over my boat and he mucks face down. Because he called so quick I am wondering if I could have gone to like $175-$200 here and still expect to get called?