Playing Ace, Four in the Big Blind - $25NL

I am just curious if anyone disagrees on this question:

You have Ace, 4 offsuit in the Big Blind with three limpers in a somewhat typical 6 max game on Party. You check your option and the flop comes 2, 3, 5 - rainbow.

You have $62 in front of you, and the Button has $25.

The SB checks, you bet the pot for $1, CO folds, and the button min-raises to $2. The SB folds. You pop it to $6, and the button min-raises yet again.

The only read on the button you have is that he is very loose and plays a lot of pots. He could easily have a smaller overpair or a set, but you really think he would have raised preflop with a pocket pair given his prior loose aggressive play. If he were trying to just make a total bluff here, he would not be min-raising.

Given the facts as stated, is there anyone here that would not push here? You can't just call here, obviously.

Does anyone fold? That seems so incredibly weak-tight to me.

Results are irrelavent here - I want to know if anyone would not push here. I think this is an easy answer, but I want to get some confirmation - or maybe learn something new.

Thanks!