I used to pull a rather large trailer with my 750 Super Sport back in the 80's. One with a large car top carrier on a metal trailer frame. I pulled it in some awful weather with that much lighter bike, and every time it made the bike more stable. IN fact there were bad days I needed to go somewhere, I would put some stuff in the trailer and take it to make the ride better.
Now I have an '04 1800 and pull a Bushtec trailer and hardley know it is there through some unusual conditions. I won't say what all trailers will do but if you are concerned about handling, get a Bushtec because it is like not having anything behind you at all, handling is great.