Does the trailer look visibly low on one side when viewed from front or rear? Your eye should pick up anything more than a couple inches of difference, if it is indeed that much.
However, I doubt if a side-to-side imbalance would have much effect on towing behavior. Among possible causes of unruly towing, that has to be far down the list. When you have an opportunity, get the trailer weighed and try to get separate weights for each side, so that you have some real data to work from, but it's probably not a significant factor in towing manners.
The #1 influence on trailer tow behavior is tongue weight. Too little is the most likely to cause problems, sway and poor tracking behind the tow vehicle. 10-12% of the trailer actual weight is the desired amount. Too much tongue weight can affect the tow vehicle, even though it actually makes the trailer itself more docile. Excessive weight on the hitch lifts weight off the tow vehicles front wheels and can make the steering erratic. When you tighten up the chains on the weight distributing mechanism, you counteract the hitch weight by transferring it forward to the front wheels. That's probably what you did.
You need to adjust the WD (chains) to make sure the tow vehicle is level after the trailer is hooked up. You should do this once you have the trailer loaded with your normal gear. Before hooking up the trailer, measure the height of the tow vehicle at the front and rear wheel wells (distance from body to ground). It may be level or it may be slightly tilted, according to the vehicle's design. Then hook up the trailer and re-measure. Adjust the chains until you get back to the same attitude as when it was unloaded, i.e. level or the same very slight tilt. Remember that chain setting - that's what you want to use unless you make a significant change in the trailer's weight balance fore & aft. You may need to use one chain link more or less if, for example, you add a full tank of water or other major weight change.
