HOTD: Top boat misplayed

I am in position and nail a flop of J77 with JJxx. Checks to me and I put out a min bet of .02 into a pot of .12, three callers, good. Turn is a T which also double flush draws the board. SB bets .20, better! One caller (even better) then I flat call (boo!). I believe the correct line here is to min-raise. I did have one player behind me but and am not sure if they would call. The best case is that they would shove if they had something like TT or T7 in which case they are coming over the top of me anyway. Anyone willing to commit .20 on a paired board should be willing to commit .20 more, if not re-raise if there is a min-raise back to them. Anyone on one of the flush draws will pay nothing on the river if they miss which is more likely than them hitting and stacking off. River is Qh which does not complete either flush. Both check to me and I make a minor value bet which gets called by the SB with the formerly nut straight who slowed down when a higher straight was possible. Though I didn't win the minimum I do think I cut into that hand's potential.