2 river value bet questions

[Municipal Hare]

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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?

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I'll dissent and say check. Scared K9-KQ makes up a fair chunk of his range – those expecting an unknown to always checkraise these or donk a big street into the PFR and 3-bettor should review the action – plus 87s, 88, and diamonds all got there. Certainly in-betweeners like 99, 66, and split sevens are reasonable too, but do they combine to outweigh the feared hands?

I also don't get the flop donk.