With JJ, on most flops there should actually not be any overcards, especially if your opponent calls you with something like AK, KQ, AQ, then the chances for overcards appearing are that much less. JJ and TT are very profitable hands, and I play them preety much the same way ( they have very similar EV) If you are the aggresor and come out betting 4-6xBB preflop and make a 6-8xBB raise after flop even if you see a A K or Q you will win more than half the time making it a profitable play picking up a couple of BB's. You most likey wont win any big pots with this unless you make your trips and your opponent hits his card, for example he has AK, you with JJ, flop comes A J X.
But you should at least be more confident with your JJ or TT they are very powerfull hands and pick up most pots unimproved.