Will the Apple store at the summit in Birmingham Alabama be open this weekend .

It appears that the answer is no.

https://www.apple.com/retail/thesummit/

Governors cannot force stores to open. They are relaxing the restrictions nd allowing stores to open if they choose to do so.

This is a world wide user-to-user technical help community. We have no idea if a specific store will be opn. Contact the store and ask them.