Since Weaver lost his starting job I'd say go ahead and drop him for Buehrle. I picked him up recently as well. I'm probably not going to start him much in June and the start of July since the Sox have a pretty tough schedule:
3 at AZ, 3 at LA, 3 vs SF, 3 vs SD (as much as it pains me I'll be starting him if he pitches during this series, hehe), 4 vs Bos, 3 at Cubs, 3 at MN, 3 vs Cubs, 3 vs MN.
After that they have it easy for the rest of July:
3 at TB, 3 at Det, 3 at Cle, 4 vs Det, 2 vs Cle, 2 at Tor, 3 vs TB, 3 at KC
August and Sept are tough, but hopefully by then Buehrle, and the rest of the Sox, will be grooving by then. That easly July should get them fired up I hope.