While we do not currently have a trailer behind our rig, in every discussion we've had about getting one a basic consideration is make the trailer tire size match the truck tire size. it only makes sense.
Kinda.
My primary tow rig is a Jeep TJ with the 2.5/five-speed, 4.88 gears, 33" tires (heavy 285/75/16"). Pulling my trailer is a bit of work for my TJ. TJ has a bolt pattern of 5 on 4.5". Current TJ tires are Mickey Thompson Baja Boss AT ("E" rated tire with three ply sidewalls - heavy tire).
My trailer has the same bolt pattern as the TJ, but the tires are an LT235/75/15" tire. I carry a spare for the trailer on the back of the trailer. They are a much lighter (and less expensive!) tire than what the Jeep's running. The axle under the trailer is mounted under the springs, and it rides level. And I've got quite a few more inches of clearance under the trailer's axle (3500lb axle) than I do under the TJ's rear Dana 44 pumpkin. I could put the trailer's spare on the TJ if I had to, but there's not enough clearance on the trailer for me to mount the TJ's spare on the trailer (axle isn't wide enough, and it would be close with fender clearance even if it was).
My other two tow vehicles:
1. 1996 Dodge Ram 1500 4x4. Same size 285/75/16" tires as the TJ (different brand though now - Kuhmo AT 51's). And different bolt pattern (5 on 5.5").
2. 1946 Willys CJ2A. 31x10.5x15" tires. And a different bolt pattern than the trailer (5 on 5.5" for the Willys).
So for me, it is easier on the TJ and Willys to carry a dedicated spare on the trailer so no matter what's pulling it, I've got a matching spare for the trailer. The truck hardly knows the trailer's back there.