Does armor weight matter with custom (orange) gear?

Heavy armor has more armor value than Medium or Light armor for a given Armoring mod.

The reason you're getting two options is because the Jedi Sentinel can only use Medium armor — so if the quest only gave Heavy armor, half the jedi wouldn't be able to use the reward.

There has been rumblings down Bioware's pipe that, in the future, all orange armor would auto-adjust to whichever tier is appropriate for your character. Currently there are some Adaptive Armor sets from the Cartel Market, social vendors, and the like that automatically adjust to the heaviest setting your character can use; folks can start tanking in Slave Girl outfits. (Heck, Shadows / Assassins already do!)