All the weight on mine is at the rear, i have experienced front wheel "float" especially when i lean back, no steering! as far as wobble goes that sounds like the the the front end is not tightened down enough?
I have aggressive tires but no shake even at high speeds, i have noticed it while walking the bike and a leaning it around a turn. mine are hybrid, on/off road so A could be right about the tires.
I had a cut sidewall and put a small piece of old tube in to seal it, it was like driving with a concrete wheel, everything was out of wack!