Possible bearing, they usually drone when loaded, I would check the condition and pressures of the tyres first, get under and look at the inside walls aswell
If not jack it up and check for play in the wheel bearing, grab at 12 and 6 o clock and 3 and 9 o clock and try to tilt the wheel back and forth
the weights missing would only cause steering wheel shake, probably just the position they were in befiore new tyres and a re-balance