Unless your shocks are really shot, they are not likely the cause of your problem. If they are completely shot, they will rebound repeatedly (bounce) after pushing down hard. Weak shocks, with insufficient spring capacity or insufficient shock damping can cause that issue, but if you don't have an early '13, or if you do and the front shocks were already replaced, that is not the likely cause here. The inability to adjust the '13 spring tension to adjust for differences in rider weight is a problem, so a very heavy rider could have troubles where others do not. The faulty front ball joints on the early '13s could do it, but if they were replaced or if the Spyder was from later production, that is unlikely.
The most common cause of that problem would be insufficient toe-in. An alignment would cure that, of course. If the Spyder follows every littly bump or change of grade in the road, it likely needs alignment. Other possibilities include suspension defects or worn parts, or steering geometry (design) issues. Those would eventually show up in odd tire wear, similar to alignment problems, as time passes. Another common cause is rider input. Gripping the handlebars too tightly, trying too hard to control every tiny wobble or drift, or "white-knuckling" can in themselves cause the problem to escalate to the point that it becomes scary. The Spyder steering is normally very precise and very sensitive, so it takes very little input to send it wandering all over the road, as you correct and counter-correct. Not saying you are doing that, but it has been a cause or an aggravation for many.
If it were me, I'd get an alignment first...preferably an Outlaw alignment. If you suspect the shocks or the ball joints, see your dealer about replacement. Have another experienced Spyder rider ride your Spyder and see if that person feels the same. Ride a demo or another owner's Spyder and compare. A Spyder that is right can be ridden readily at 100 or more with one hand on the bars (don't ask how I know). If yours is not stable, the cause should be carefully investigated and corrected.
