Villain is 45/9/1 and I just saw him push all-in on a busted OESD on the river a few hands ago.

PokerStars No-Limit Hold'em, $0.10 BB (8 handed) from (Format: FlopTurnRiver)

UTG+1 ($8.75)
MP1 ($3)
Hero ($12.15)
CO ($9.75)
Button ($4.80)
SB ($5.15)
BB ($2.40)
UTG ($12.45)

Preflop: Hero is MP2 with A, J. MP1 posts a blind of $0.10.
2 folds, MP1 (poster) checks, Hero raises to $0.4, 1 fold, Button calls $0.40, 2 folds, MP1 folds.

Flop: ($1.05) 7, 4, 5 (2 players)
Hero checks, Button checks.

Turn: ($1.05) 5 (2 players)
Hero bets $0.7, Button calls $0.70.

River: ($2.45) T (2 players)
Hero checks, Button bets $1, Hero calls $1.

Final Pot: $4.45

I don't mind the delayed c-bet on the turn if you think villain will fold if he has nothing, but I don't like the river call. You said he shoved a busted draw earlier...this looks like a donkish value bet or a blocking bet. Who knows.

Try not to make calls like this. (I caught myself doing this the other day. ) Yeah, sometimes they bluff you off a small pot, but that's good because it'll give them the idea that they can keep doing it. Eventually you will stack them (or the next guy) and that'll more than make up for small pots like this you "let them take away".