Flopped A Set... Did I Miss A River Bet?

Let me start off by recognizing that my preflop call with 8-8 was probably poor given that the pot was small. I probably should have either raised or folded preflop. My focus is on the river. I think I should have raised on the river. Let me know what y'all think:

10-handed $5/$10 Limit Holdem on PartyPoker

Hero is in the cutoff seat with 8 [img]/images/graemlins/heart.gif[/img] 8 [img]/images/graemlins/club.gif[/img]

5 folds, LP calls, <font color="red"> Hero calls </font>, Button calls, SB folds, BB checks

Flop (4.5 SB): K [img]/images/graemlins/club.gif[/img] T [img]/images/graemlins/spade.gif[/img] 8 [img]/images/graemlins/spade.gif[/img]

BB checks, LP checks, <font color="red"> Hero bets </font>, Button folds, BB calls, LP calls

Turn (3.5 BB): K [img]/images/graemlins/spade.gif[/img]

BB checks, LP checks, <font color="red"> Hero bets, BB raises </font>, LP calls, <font color="red"> Hero 3-bets, BB caps </font>, LP calls, Hero calls

River (15.5 BB): 5 [img]/images/graemlins/spade.gif[/img]

<font color="red"> BB bets </font>, LP calls, Hero calls.

I only called here, fearing that either BB or LP had Kings full of Tens or perhaps quad Kings. In hindsight, I'm thinking I should have raised, and if BB 3-bet, I would just call. Thoughts? Below in white are what BB and LP had:


<font color="white"> BB had A Spades 4 Spades
LP had Q Spades J Spades </font>