Rule of Cool prevails!! I like it! I let Goliaths throw rocks as a feature, it's volleyball/basketball sized and does 1d10 bludgeoning damage, 20/60 range. If they are a Rune Knight, or Path of the Giant Barbarian now, it doubles when large and triples when huge, per DMG oversized weapons.
I LOVE this background so much! I am playing an Eladrin Rune Knight Fighter who was raised by cloud giants and there is a weirdly beautiful marriage of features going on.