Sulfotransferase that utilizes 3'-phospho-5'-adenylyl sulfate (PAPS) as sulfonate donor to catalyze the transfer of sulfate to position 6 of internal galactose (Gal) residues of keratan. Cooperates with B4GALT4 and B3GNT7 glycosyltransferases and CHST6 sulfotransferase to construct and elongate disulfated disaccharide unit [->3(6-sulfoGalbeta)1->4(6-sulfoGlcNAcbeta)1->] within keratan sulfate polymer (PubMed:17690104, PubMed:9405439, PubMed:10642612). Has a preference for sulfating keratan sulfate, but it also transfers sulfate to the unsulfated polymer (PubMed:9405439). Involved in biosynthesis of phosphacan, a major keratan sulfate proteoglycan in the developing brain (By similarity). Involved in biosynthesis of 6-sulfoGalbeta-containing O-linked glycans in high endothelial venules of lymph nodes. May act in a synergistic manner with CHST4 to generate sialyl 6',6-disulfo Lewis X motif, a recognition determinant for immune cell receptors implicated in leukocyte trafficking (PubMed:10330415). Catalyzes sulfation of N-acetyllactosamine (LacNAc) oligosaccharides with highest efficiency for sialylated LacNAc structures (PubMed:10642612). 3'-phosphoadenylyl sulfate + keratan = adenosine 3',5'-bisphosphate + keratan 6'-sulfate. Glycan metabolism. Widely expressed at low level. Expressed in brain and skeletal muscle. Expressed by high endothelial cells (HEVs) and leukocytes. Belongs to the sulfotransferase 1 family. Gal/GlcNAc/GalNAc subfamily. Was originally (PubMed:9639683) thought to be the ortholog of chicken CHST3 and therefore named C6ST. However, it has no strong chondroitin 6-sulfotransferase activity.