As pointed out above, these tires often do not seat correctly on the plastic wheel rim first time. Soapy water applied with paint brush in the rim-to-tire gap of a deflated tire will help seat the tire bead correctly when it's re-inflated. Rinse, then let the water dry before spinning up the wheel because you want a firm grip of the bead to the rim seat, and don't get any water inside the tire
If the tire still wobbles, then try a new tire and/or tube. These are low speed wheels, and the production variations on carcass distortion and tread thickness won't be to the same standards as a high speed tire like an auto tire.
Relative to the tire misalignment or distortion, the valve stem won't be contributing much to the out of balance because it's at a much smaller radius, plus the rim is lighter where the valve goes through (because of the hole), and this partially compensates for the weight of the valve and valve stem.
Please be very careful adding balancing weights. If they get loose they will be a high speed projectile. If the tire won't balance itself, I'd say it should not be spun at speed as the out of balance probably indicates some sort of carcass "fault".
Graham.