I can't think of a lot of situations where I would fold a pocket pair pre-flop in short-handed NLHE, when no one has raised ahead of me. As long as my opponents and I have reasonable stacks (improving implied odds) I'd probably limp in here and see if I can flop a set.
You're probably thinking in the right direction, however I'd never fold 44 there because if the table is beginning to think you are full of it you can easily get someone's stack if you hit a set.
What is right about what you are saying is that due to your table image you might drop a few hands off the bottom of your raising range and fold them, for example hands like A9, KT, QTs, that kind of stuff.
It is good that you are thinking about table image.
I limp with them, sometimes min raise. So many people fear the min raise that they don't reraise unless they have a monster. Then if you catch a set you are in good position to win a big pot. That being said, I am very new so this may not be the best advice.
This is a great situation to raise. As mentioned above your table image in the past few hands maybe a little loose. Your implied odds are good here if you hit your set as you will be played back at a little more than usual allowing you to extract more value. low pp's are easy to dump when you miss the flop, you want to keep your loose image up to protect your good hands.
