two pair on the river, call check raise?

[Fathomer1977]

Full Tilt Poker, $0.05/$0.10 NL Hold'em Cash Game, 6 Players
LeggoPoker.com - Hand History Converter

Mp is 44/6/7, BB is 23/15/3.4

UTG: $4.60
MP: $7.85
CO: $10.80
Hero (BTN): $9.05
SB: $20.05
BB: $13.10

Pre-Flop: T[img]/images/graemlins/diamond.gif[/img] J[img]/images/graemlins/club.gif[/img] T[img]/images/graemlins/diamond.gif[/img] J[img]/images/graemlins/club.gif[/img] dealt to Hero (BTN)
UTG folds, MP calls $0.10, CO folds, Hero calls $0.10, SB calls $0.05, BB checks

Flop: ($0.40) 5[img]/images/graemlins/club.gif[/img] 2[img]/images/graemlins/club.gif[/img] 7[img]/images/graemlins/spade.gif[/img] (4 Players)
SB checks, BB checks, MP checks, Hero checks

Turn: ($0.40) J[img]/images/graemlins/heart.gif[/img] (4 Players)
SB checks, <font color="red">BB bets $0.30</font>, <font color="red">MP raises to $1.30</font>, Hero calls $1.30, SB folds, BB calls $1

Should this have been a pot sized bet or fold situation?
MP could limped with KJ, QJ, or possibly AJ, but has an aggression of 7.

River: ($4.30) T[img]/images/graemlins/spade.gif[/img] (3 Players)
BB checks, MP checks, <font color="red">Hero bets $1.50</font>, <font color="red">BB raises to $8.80</font>, MP folds, Hero ?

What hands make a check raise on the river? A set on the flop should have bet to get the draws out. He lead out on the turn and called a reraise, so if the jack helped him, at best he has two pair there and thinks he's still ahead.

[TheSalche]

Fold turn, fold river. This looks like a poorly played set.