The feat is available during level-ups taken after player character mutates, and presumably should boost critical multiplier of claws as these are either fist weapon or unarmed, or possibly even hammer for Huge Claw - but no increase to it is shown in combat stats, and practical testing confirms it: just did 399 damage crit with a Huge Claw, while under circumstances if Heavyweight would work - then any crit made would be 440sh or higher damage (for having not 125%, but 175% crit multiplier for Huge Claw).
Screenies with relevant data attached. Minimum crit damage with Heavyweight working - would be 162 + 162*175% = 445.5 damage. Couldn't be 399 if it works and just not shown in Offense stats.
P.S. I suspect that Improved Unarmed Combat and Expert Unarmed Combat feats do the same: while available in mutant form, it does not look like they work. If it's intended that these feats don't work, then the bug is that they remain available for taking while playing as a mutant - a waste of feat points, if they do nothing as intended.