playing on bo dog mtt blinds are 10 20 im in big blind and a player from late position raises to 60

I end up calling with q j and the flop comes out q 5 6 with the 56 being diamonds. I check to the raiser and he bets 120 and I smooth call. First of all, should i have put in a raise?

Next card comes another queen making the board q 5 6 q ? I am unsure at what he really has so what is the right situation here do i check or do i lead out and bet some?

mellyy85