2 river value bet questions

[private joker]

I haven't played online in a looooong time, so I'm really rusty; this is like my second week back at 5/10 short.

Hand 1: BB is relatively unknown but is playing on at least 2-3 tables FWIW; Button is kind of weak and plays straightforward postflop:

PokerStars $5/$10 Limit Hold'em - 6 players
Hand Converter Tool from DeucesCracked.com

Preflop: Hero is CO with T[img]/images/graemlins/heart.gif[/img], T[img]/images/graemlins/diamond.gif[/img]
UTG folds, MP folds, <font color="#FF0000">Hero raises</font>, <font color="#FF0000">Button 3-bets</font>, SB folds, BB calls, Hero calls.

Flop: (9.40 SB) 4[img]/images/graemlins/spade.gif[/img], K[img]/images/graemlins/diamond.gif[/img], 7[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(3 players)</font>
BB checks, <font color="#FF0000">Hero bets</font>, Button calls, BB calls.

Turn: (6.20 BB) 2[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(3 players)</font>
BB checks, <font color="#FF0000">Hero bets</font>, Button folds, BB calls.

River: (8.20 BB) 8[img]/images/graemlins/diamond.gif[/img]
BB checks...

Is this a check or a bet/fold?

***

Hand 2: I hardly ever limp PF but this seemed like the spot. The limper is super-fishy and the blinds are fairly loose; I wanted to get in the pot on the button, but didn't think I had enough hand to raise and preferred to see a flop and then evaluate from there. BB in this hand is new to the table, no read or stats.

PokerStars $5/$10 Limit Hold'em - 6 players
Hand Converter Tool from DeucesCracked.com

Preflop: Hero is Button with 8[img]/images/graemlins/diamond.gif[/img], J[img]/images/graemlins/diamond.gif[/img]
UTG folds, MP folds, CO calls, Hero calls, SB folds, BB checks.

Flop: (3.40 SB) 6[img]/images/graemlins/spade.gif[/img], J[img]/images/graemlins/club.gif[/img], 5[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(3 players)</font>
BB checks, CO checks, <font color="#FF0000">Hero bets</font>, <font color="#FF0000">BB raises</font>, CO calls, Hero calls.

Turn: (4.70 BB) 5[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(3 players)</font>
<font color="#FF0000">BB bets</font>, CO calls, <font color="#FF0000">Hero raises</font>, BB calls, CO calls.

River: (10.70 BB) 7[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(3 players)</font>
BB checks, CO checks...

Bet/fold? Check? Bet/call?