Both......the steering stabilizer is leaking and will be replaced shortly, but it also seems to me that the stock shocks aren't capable of dealing well with the added weight. On a racing motorcycle, I would increase the viscosity of the fork oil if I had added weight to the bike (or to myself
) and this type of problem would be solved. Without the option to do the same thing on the Jeep, I'm thinking new shocks might be in order.
As far as the bump steer thing goes, will weight sag cause the track bar and drag link to get out of parallel? And by parallel, I assume that you mean in a static position (parked). Yes?
First visualize the track bar connected to the chassis at one end and to the axle at the other end. Then, as the axle moves up and down, the end of the track bar that's attached to the axle will swing in a large arc. That means that the axle itself has to move slightly to the left or right (following the arc) as the axle moves through its full range of vertical motion.
The drag link is also attached to the chassis at one end (well, sorta through the Pitman arm and steering box) and to the steering knuckle at the other. As the axle and knuckle move up and down, they force the knuckle end of the drag link to move up and down, too, which means it also swings in an arc and the knuckle end moves slightly left or right. This motion trys to pull or push the steering knuckle left or right. If it does, that's the same as you turning the steering wheel, it causes the vehicle to veer one way or the other and it's called bump steer.
However, if the arc that the drag link swings on is exactly the same as the arc the track bar makes, then the two effects cancel eachother out - the axle moves, say, left due to the track bar arc, but the drag link swings on the exact same arc, moving left just the same amount, so the steering knuckle remains straight - no steering input, no bump steer.
If the drag link and the track bar are the same length and are parallel at any point, they will remain parallel through their entire range of motion - a basic property of a parallelogram. So, if they were equal and parallel at stock ride height, they should be parallel even with sag.
Unfortunately, for our vehicles, the drag link is quite a bit longer than the track bar (about 41" vs 33") so even if they are parallel at ride height, they won't be at extreme compression or droop.
My guess is that on a stock vehicle, both the track bar and drag link are fairly close to horizontal which means that they are operating on the least sensitive part of the arc. Lifting (or sagging) makes both operate off horizontal and in a more sensitive part of the arc (more lateral movement per inch of vertical travel). So, your situation could introduce some bump steer, but I would doubt that you'd see very much with the numbers you are talking about.
Castor (lack of) and toe out can also make a vehicle somewhat "darty" going over bumps. If you've done anything that would have modified these, you might want to have them checked.
Sorry for the long discussion, hope that you find the problem. By the way, mine drives something like a pig on the street and was prone to wander a lot even when bone stock - you may end up having to live with some quirks.