I was about to accuse scaredypants of a Physics fail, then I started typing and I remembered thermodynamics.. but I was always rubbish at it..
PV = nRT
So if P and V are the same (same pressure in your tyres, same R and temperature, then n must be the same too right? Or almost the same.. because they'd both be similar to an ideal gas…
But n moles of helium would have less mass than n moles of air, by fair bit since a mole of helium is only 4g and a mole of air would be what.. 15g ish? So the density of gas in your tyres would indeed be much lower hence reducing the weight (due to buoyancy) and the mass would be significantly less, around a quarter.
So maybe scaredypants was a physics fail. Or maybe it's me.. 🙂