how to interpret a min raise

[Temp Hutter]

Day 1 WSOP ME
200-400 level
New player at the table raises on the button to 1,400. I have 88 in the BB. I ask the player to lift his hands so that I can see his chip stack and I give the impression that I am contemplating a raise (although I was not). I call the raise and the flop comes AK4 rainbow. We both check. The turn is a J and I bet 2,500 into a 3,000 pot. Button min raises to 5,000.

Does the min raise mean something big like AK or something weak like Ax or TT? What is your play from here? Hero has 35K behind and villian has another 18K behind.