Unless you're training seriously for something I see no reason why you can't ride on the weekend if you enjoy it. If you're just a bit tired on Monday, no big deal. Just take it easy on the ride to work and back. You can ride 12 miles at a leisurely pace and still get there in a reasonable amount of time.

I commute to work 12 miles each way as well, and while I don't usually ride on the weekend I do run on the weekends, and yeah, I'm tired on Monday, but nothing that's going to keep me from riding to work.