Breastfeeding Advice needed.

My son is 3 weeks old. Breastfeeding is going okay except at nght it seems like he just can't get full and just eats and eats. I know it's normal for newborns to wake every 2-3 hours around the clock to eat but sometimes he wants to eat every half hour or hour at night and sleeps more during the day. The past couple of nights when he just couldn't get full I gave him a bottle with pumped breast milk and he slept for 3/ 4 hours straight which is a long time for him at night, I think because his belly was finally full and he was able to relax. Plus it was a nice sleep for me also! I am just starting to pump and don't think I can pump enough to give him a bottle every night and am considering just replacing one night feeding with formula to help us both get that little extra stretch of sleep. Opinions please?

I should also mention when I go back to work in about 6 weeks I work night shift and he will be getting bottles then too. Not sure if it will be breast milk or formula though.