Wobble since day one only means it was there for a long time...does not make it right!!! Something is wrong, so you have to troubleshoot methodically. Could be something as fundamental as steerer tube angle not quite right when welded up at the factory, but I would bet on something more common like wheels and tires, steering bearings or the like.
Start with tire pressure 2 or 3 lbs at a time up or down from nominal, see if it gets worse or better if over or under inflated slightly at the speed(s) in question. Next check tire/wheel balance; then tire and wheel alignment, wheel bearings & cups, the forks (stiction and oil level, proper rebound/compression dampning), steering bearings (preload and fork fall away), frame alighnment, cables and wiring dressed properly,the handlebar mounts (if rubberized) and finally verify that the back tires (surprise-surprise) are also pressurized properly/balanced and aligned. Funny how a motorcycle being in such a high state of tune can require only minor tweeks to get things right or wrong in short order.
Been down this road too many times on metric sportbikes, which are even more sensitive because more weight is on the front with rake and trail figures much more radical so just minor changes in suspension, tires and brakes can affect handling much more serverely making steering dampners and fork braces necessary to stop tank slappers from occuring.