Villian's been at the table for about 20 minutes and he's limping into every pot. Never raising, calls all raises PF. Bought in for $300. Has called down and lost a couple of pots outkicked or folding rivers. All of the pots he's won, he's just shoved the turn or river and taken the pot. I've been fairly aggressive, but positional in general- definitely not punishing limpers too much or re-raising much PF and playing more postflop.

FTP's connection's been horrible for me this week and the HH's are saving in partials.

Blinds: $1.5/$3

Hand #1-
Villian has ~$210. I cover.

OTB
Folds to me. I raise to $10.50. Villian calls in the BB.

Flop (~$22): :[As]
Checks to me. I bet $16. He raises to $60 with about $140 left behind him.

Hand #2 (same Villian)
Villian has ~$320

UTG+1
Folds to me. I raise to $12. Villian calls OTB as does the BB who's a solid player and has ~$550. I cover.

Flop (~$36): Q 5 rbw
BB checks. I bet $28. Villian calls. BB folds.

Turn (~$92):
I bet $66. Villian pushes for around $280. It's $211 and change to me with about $440 in the pot.

Hand1. I would play for it all here. Ax is likely for such a villian. I would push now, as lots of turn cards are bad.

Hand2. I would check turn very often >70%. (Did you plan on checking behind on the river?)
With this action I would fold. In my experience he has a 5 here very often. Moreover I prefer that someone else finds what his pushes mean. (Or I prefer to have a less mrginal hand here.)