w/o any draws I like a check raise here. If no one hit the T as well it will probably be checked around and you know your hand is most likely good. If someone has a better T and is sandbagging you will keep the pot small and it won't punish you if you are beat. If someone else bets the flop, make a pot sized raise and if he min raises you i'd consider dumping the hand. I mean what are they going to have on a flop of TT6 rainbow? a pair of 6s?? I don't think a pair of 6s would min reraise you here. An overpair would probably have raised preflop so you are probably not facing one. Betting here gives you no new information so I perfer the check/raise.
All that min raising that this guy makes is mighty fishy. I might even do a check/call if he bets small on the river instead of firing out a weak bet. You are asking for a raise and if he has nothing his raise won't be a minimum raise. If he is bluffing he will make a huge bet, one that you can't really call unless you want to lose your whole stack the 90% of the time he isn't bluffing here...

In this hand you are in a bad situation and he has taken control of the hand. If you thought your hand was good on the turn you should have reraised to take back control and if you thought it was no good why are you putting more chips in?