You don't specify the Tundra's payload capacity. Typically Trailmanors have a high tongue weight. If you add that tongue weight to your 650# motorcycle + people and gear in the truck, you may exceed the Tundra's payload capacity and GVWR. I know I did that with my Tacoma (without a motorcycle).
The payload and motorcycle will not affect what your hitch can carry, but I wouldn't be surprised if your trailer's hitch weight exceeded the 500# limit. For that reason alone, you may want a Weight Distributing Hitch.
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