The Honda owner manual says to trailer with the motor down, using a support brace. I've never done that, and always trailer in the up position, after backing the motor tilt off to put a little preload on the two rotating support legs, while still keeping the tilt cylinders engaged, and therefore capable of taking a little force. The dealer told me to do it this way, and it makes sense. No damage has resulted after extensive trailering, and I don't like the thought of dragging the lower unit. I'll trail a strip of bright surveyor's marking tape tied to the prop, and seeing that at eye level has so far discouraged any other drivers from rear ending me.
As to weight on the transom, the weight of the motor is the same, no matter what position it's in. Therefore, the transom has to exert the same vertical force in each position. Essentially, the motor wants to compress the transom by pushing it down, and the transom exerts an equal vertical force on the motor. The angle of the transom from the vertical complicates this somewhat, but not all that much. The effect of the angle off the vertical is to introduce a twisting force on the transom.
However, when the engine is in the down position, all of the weight of the motor times the distance of the motor's center of gravity from the transom, exerts a moment (torque) force on the transom, which attempts twist the top of the transom off, toward the rear. With the motor in the elevated position, the head of the motor is in front of the transom, while the lower unit is extended to the rear. I haven't done a big calculation, but would be willing to bet that the moments of the head (now wanting to twist the transom forward) and lower unit (still wanting to twist the transom aft) cancal each other out to the extent that the net moment, and therefore net twisting effect on the transom, is reduced by trailering in the up position.
So, I'll just keep on truckin in the up.