Set of kings, check my river play

[checkmate36]

Ultimate bet .05/.10 full table.
I guess I shut the table down before the hand history could be transferred to PT.

Hero is UTG with KK.
Villian is in MP1 and is a tight player and BB is fish.

Hero raises pre-flop and flop comes Ks 2h 3h. BB checks and I bet, both call. Turn brings Td betting goes same way.

River brings the 3rd heart. BB checks, hero bets planning to call a raise. MP1 raises, BB folds, hero calls.

Should I have just check/called? I was thinking the correct line was bet and call a raise. Thanks for any help and sorry I couldn't get the exact hand history for this post.