I do weights and commute on the same day, but I have a short commute. I really have little choice. Since the bike is my primary transportation, I have to ride very day. A rest day for me would still entail at least 40 minutes of easy riding.

Even so, I think crosstraining is vey important. In addition to weights, I walk or hike at least once a week and I row in the summer (in a real boat).

Cycling doesn't do any good for the skeletal system or even for any muscles above the hips. It also overtrains the quadriceps relative to the hamstrings.