Towing with a 1955 Ford Panel Truck

I have a 55 Ford Panel with 350 crate, 700R4 and a nine inch Ford rear end on leaf springs. And it sways when towing my motorcyle trailer. Any suggestions?

 

Is it stock? We really need a lot of underside pictures.

 

Welcome to the HAMB from Illinois.

I'd start by checking the shock absorbers on the truck and trailer.

 

Not enough tongue weight? That’s the main thing that I have seen cause sway in a trailer.