villain looks fairly passive. passive villains check call their draws.
how does he perceive you? if you appear super aggressive then he might think his KJ is good. but i don't think a passive villain check raises KJ.
if you had TPTK and the board was 3s Ad 4s... i'd say stack off heads up... as weaker A's will likely pay you off.
i usually respect a check raise from a passive villain.