PDDGM,
I'm certainly no mathematician but, I think if someone on here that has maybe some geometry back ground which, would include calculations in and on fulcrum loading, distances, leverage, and more could tell you EXACTLY what and won't be displaced, based on weights and placement. I mean, I hated math in High School but, I've had to use it my whole life and sure wish I'd have paid attention back then.
But, a very simple way to look at is a child's "teeter-totter". Two kids, the same exact weight, sitting the same exact distance from the center of the fulcrum point should, and most of the time DO, off-set each others weight. But, if one of them is heavier than the other, then the obvious is going to happen. But, move the heavier one in towards the center a bit and then, it becomes more and more equal.
So, my point is, weigh the front of the car, weigh the bike, and position, ON PAPER, the two weights, at calculated positions at the distance intended for each from the center point, which is directly over the axle. There must be some sort of formula that can tell you EXACTLY what will happen and, what kind of tongue weight will be expected.
But, the point is, knowing the exact weights of both and, what the exact weight of the tongue of the trailer/dolly will be (empty). From that point, I would figure any math major or, anyone with an engineering degree could come up with an answer in about 5 minutes.
At that point, you'd know almost to the pound what to expect. At least that's the way I'd go about it. Good luck.
Scott