What midna said
I express far less than my LO gets from my boobs. I'd let him feed from your boobs only to build a better supply rather than express and feed it that way. Yes it will take patience and a bit of time and probably a grumpy baby for a little while but it will get your milk supply flowing better and he'll end up feeding better off your boobs. Chances are he could get more off your boob himself and therefore would not be feeding every 2 hours probably.
Babies feed ALOT in the early weeks, as others have said they are glued to your boobs. There is a reason for this and its all natural and baby is doing his bit to get your supply going properly. Having him suck stimulates your supply also.
My LO was feeding every hour at that age. Emptying my boob each time and sometimes needing the other boob. He is still feeding every 2-3 hours during the day and getting about 6 ozs off a boob. I can only express about 4 tops. But he takes what he needs from me and thats the important thing. I have the milk there for him.
Don't feed water to fill him up as breastfed babies don't really need it. Your foremilk (the first minute or so) is the thirst quenching part of your milk for your baby) then comes the hind milk, which is the rich tummy filling stuff.
And there is not really anything to worry about re him getting overweight. Let him tell you how much he needs. He is your guide. Each baby is different and if he is wanting more, then let him feed.
I personally would cut out the formula, go have a couple of days in bed with baby, skin on skin and just feed him off the boob and not express. Let him get the milk going and fill his tummy as and when he needs it.