J.C.
Hi Heather,
Yes, your body will adjust to his schedule. Your milk supply will slow at night and be normal during the day. Don't expect him to sleep through the night though from here on out either...7 weeks is early! But it does happen! Mine were both 9 months old. :(
To help the spit up issue you can pump or hand express a little "off the top" before his first feeding in the morning. This will also help him fill up with good stuff and not so much foremilk which can make him spit up and is not filling and may leave him still hungry and wanting to feed again in two hours.
Best of luck and happy dreams! :)