Pseudocompact topological group refinements of maximal weight

It is known that a compact metrizable group admits no proper pseudocompact topological group refinement. The authors show, in contrast, that every (Hausdorff) pseudocompact Abelian group G = (G, T) of uncountable weight alpha, satisfying any of the following conditions, admits a pseudocompact group refinement of maximal weight (that is, of weight 2(\G\)): (i) G is compact; (ii) G is torsion-free with alpha less than or equal to \G\ = \G\(omega); (iii) [CCH] G is torsion-free. Remark. (i) answers a question posed by Comfort and Remus [Math. Zeitschrift 215 (1994), 337 346].