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Yes it does, but not by enough to really make a difference.
With 3" I agree.
The load rating is based on multiple factors. Sitting still with a static load, then it makes no difference at all. When you're moving and subject to lateral forces then there is an effect. It's the same effect you get when hauling something that rocks or sways back and forth. There is also a slightly greater effect if the weight of the load isn't evenly distributed. The bias of the load is slightly exaggerated by the 3".
As long as you aren't pushing limits, you're fine.