10NL: River decision vs. bad lag

[Lurker.]

Villain is your typical 10nl bad lag. 3bets light, uses the pot button a lot, stacks off light. I've been raising at the table a lot, but folding KQ type hands to 3bets etc a lot. I'm mostly talking about the river here, but thoughts on all streets welcome.
Viallain has 100bbs and Hero covers
Preflop:
3 folds, Hero raises to $.35 with A /images/graemlins/spade.gif9 /images/graemlins/club.gif, sb calls and BB calls.
Flop: A /images/graemlins/club.gifJ /images/graemlins/spade.gif4 /images/graemlins/heart.gif
SB checks, BB bets $.65, Hero calls, Sb folds.
Turn: 10 /images/graemlins/spade.gif
Villain bets $1.15, hero calls
River: 9 /images/graemlins/diamond.gif
Villain bets $4.5, Hero?

[CaseS87]

I think you miss value just calling here. Villain will probably call the rest of his chips with a good ace or any 2 pair.

[Vern]

Isn't $4.5 more than half his stack?

3.5+6.5+11.5+45 = 66.5, so he only has 33.5 bb left behind. The fact he is potting the river with more than half his remaing stack makes me think he is pot committed. If you push there will be ~166 bb in the pot, so he will have 5:1 to call. If your read is good, I push a lag right at the river because I know I am calling and he isn't folding anything but a bluff here, the fact he is likely to call with a lot of hands I beat makes the push +EV. IMHO.

[Lurker.]

argh. i only called. he flipped a10, but i do agree that by not pushing i'm losing value in the long run. thanks guys.