I've never had a rad cap that was weak not cause an overflow, especially since I live in southeast Texas where the temps get into the high 90's at night.

Make me sure you get the thing bled out properly, take it for a spirited drive around the block with a couple of full throttle romps through 2nd at least then park it and allow it to cool overnight then top off the overflow. Check it for the next few days. There are bleeder screws as well but I'm sure you already did that.

Jeff