Covers and envelopes related to divisibility

There are several characterizations of rings over which the modules admit certain covers (like injective, absolutely pure) or envelopes (like flat, torsion-free), not in the usual relation with cotorsion pairs. In this note we discuss commutative rings whose modules have divisible, h-divisible, or weak-injective covers, resp. commutative rings with weak-dimension 1 or projective dimension 1 preenvelopes. Subperfect rings and tight systems that are needed in the discussion are also dealt with in details.