I alternate between betting and checking (with the hope of check-raising if the situation is right) in this spot, with much depending upon how the table is behaving as a whole.

If I had to choose the scenario I would like to occur, it would be: Hero checks, UTG bets, 3 calls, Hero check-raises, 4 calls. Assuming you see a showdown, your pot equity is ~35%, yet you're putting in only 20% in the scenario I just mentioned, and you trapped the field for an extra bet. So, what I like to do is check and see what materializes. If, after a bet from behind me, I think I can get in by contributing less than 35% of the betting on the current betting round, then I will check-raise. If not, I call if the pot odds are correct.

However, if the table is such that it will often be checked through or it will be bet without callers, then I will simply bet in order to have some fold equity and also to perhaps disguise my hand from those who think I'm representing a pair of Kings or Jacks and are drawing to a lower flush.