Transfers a sulfate group to the hydroxyl group at C3 of non-reducing beta-galactosyl residues. Acts both on type 1 (Gal-beta-1,3-GlcNAc) and type 2 (Gal-beta-1,4-GlcNAc) chains with similar efficiency (By similarity). Strongly inhibited by Cu(2+) and Zn(2+). Protein modification; carbohydrate sulfation. Belongs to the galactose-3-O-sulfotransferase family.