Er is the term 'Heavy' a bit misleading ?
A Bag of grenades would be heavy so perhaps they would be the Big strong boys of the Regt capable of hurling the grenades a fair distance.
I once asked my uncle who had been in 7 th Battalion Green Howards, if they where Light Infantry, His reply was no Heavy Infantry.
Grenadiers were usually selected from the tallest and strongest men in a battalion they formed a company on the Bn's right flank. The Black Watch (Royal Highland Regiment) maintained the tradition (perhaps as 3 SCOTS they still do?) referring to their right flank rifle company as Grenadier Company.
Grenades were up until about 1915 a match lit fused Engineers store. The germans entered WW1 with a serviceable grenade. A bit like everything else really, just as we get good the opposition chucks in the towel!