[hagelito]

If I would have played my 44 against the $2 raise (which I probably wouldn't) I would have called it and put him on high cards or even possible a higher pocket pair wich wouldn't be very good (you never know for sure).

Then I would bet big on the flop to make it hard for him to call with drawing hands/over cards because only a higher pocket pair beats you at this time.

But as I wrote in the beginning, I probably wouldn't play this hand at all because of the possibility of a higher pocket pair.