Today's lens coatings are a lot tougher than they were a few decades ago--and in fact some of your old Weavers may not even be coated.
Plain water and clean cotton cloth work well, but a microfiber cloth is better yet, and paper made specifically for lens cleaning also works. Just make sure you wet the lenses before using the cloth.
Various "official" lens-cleaning liquids don't hurt, but aren't really necessary--and on older scopes may harm the lens mounts. The biggie is not to try to wipe off dry dust, or use paper towels, facial tissue, etc. instead of clean cloth, because they contain particles that can scratch lenses.
I use a large-ish ladies makeup brush and hold the scope with the relevant lens down, this way when I use the brush from below all the dust drops in to the bristles and don't just get rubbed around the lens.
After that I either wipe with glass' cleaning wipes or spray some camera lens muck and wipe off, depending on whether I can sneak enough of the wipes away from my wife without her catching me.
If she catches me I find it best to grin like a big country lout and play dumb...that way I still get fed.
