My main question here is about bet sizing.. bigger on turn? My main thought was just setting myself up for a pot sized river bet.. when he jams, i scratched my head and called.. obv never folding to river jam right? Villian is an unknown.
I think the size of the turn bet is OK, I wouldn't go bigger than 350-375 and no, you can't fold a set here. You just have to be good more than ~ 1 out of 4 times to make the call +EV and altough villain's line looks like value he can do this with worse like two pairs.
+1 to I<3Poker, and yea snap call on river. He can do this with a lot worse and there's also busted draws who can try to bluff. Basically there's only 45 and 88 that can beat you in his range (if he even plays them like this).
I think you have to call since there arent many things that beat you here.
Looks like he had 3A or a lower set.
The 45 was just very unlucky I think.
Nothing wrong with the way you played this.