Dan, a few things to ponder....
First, 4 tires vs 2. (or even 3 tires)...
Next, under normal controlled braking a motorcycle with a trailer will do just fine. But, add any extra excitement to the mix and things change. On a motorcycle generally most of the braking is done with the front tire. All kinda of very scientific type forces tend to load up the front tire. Even when you just use your back brake your bike will squat, applying force to the front too. And when braking force is applied to the front wheel, everything wants to pivot on the front axle (think of a "stoppie").
In a corner, things become more interesting. That 200, 300, 500 lb trailer really wants to go straight. Best way to handle towing is to brake well before the corner and apply throttle to pull the trailer along thru the turn. If you are not pulling the trailer, the trailer is gonna push you. And remember, the trailer wants to go straight.
Getting the tongue weight "right" is an interesting game too. Too much tongue weight and accelerating might lighten the front end (think of a "wheelie").
Here's another look at my old bike/trailer set up. When I'm sitting on the bike, the trailers tongue is almost level.
