1" x 2" Furring Strips for Drywall Ceiling
Weight isn't going to be your issue here. 2 inch furring strips may be pretty hard to hit with the drywall screws. The screws need to be in good solid wood and not going through an edge etc.  If You are careful, caulk some good lines, the 1X2's might work for ya.  The other consideration is if the spacing is good and you have enough surface to butt pieces of drywall together and still have wood to screw into.  I'd probably plan on adding some extra 1X3's to the mix to be sure you have good wood to catch a screw.