cap with turned 2 pair?

[ninja please]

party 2/4, just sat down at this table after my last one broke up (much to my dismay -- there was a player who called 2 cold PF with 85s, and beat my TPTK when he turned his gutshot straight)

i'm dealt Ah 8h in the BB
one EP limper, and MP raises all in half a bet. LP calls and i call, as does limper.

flop: As 5s 4c
i bet out, EP folds, LP raises, and i call.

turn: 8c
i check, LP bets, i raise, and he 3 bets.

does he 3 bet a check raise with any hand i can beat? does anyone cap here? or just call him down. i was feeling a low set or even 23 was more likely than someone 3 betting a good A or lower two pair.

i call the raise and check call the Tc on the river.

he shows A4 for 2 pair. all in shows nothing and i take the whole pot.

what's the verdict? am i too weak or did he over play?