I have no experience with utility trailers. However, for 10 years I used a modified snowmobile trailer (Triton XT single-snowmobile model) to haul sea kayaks. I recently sold that and now use a Trailex SUT-350-M2 kayak trailer.
Neither of these feels flip-prone despite having small 8" wheels. However, the two have very different designs.
The snowmobile trailer has a narrow track (space between the wheels), because that model-year trailer put the flatbed platform over the fat wheels. Outside span of the wheels was only about 4 ft. The new version of the same trailer puts the platform between the wheels, which have been increased in diameter to 12". The snowmobile trailers have excellent ground clearance due to the use of Torflex axle. Weight of mine was about 380 lbs EXCLUDING crossbars, cradles, etc. Trailer's flatbed platform is fairly low and rides within the truck's slipstream.
The SUT-350-M2 trailer wheels span about 6 ft on the outside. The tires are narrower, which would reduce stability if not for the wide track AND a low center of gravity. The meat of the trailer is in the long main beam, which sits quite low between the wheels. Not much ground clearance (only an issue on lumpy unpaved roads and abrupt transitions between level ground and extremely steep climb--think "sedan" instead of "jeep"). But it weighs only 160 lbs including the integral crossbars. The kayaks ride higher than they do with the snowmobile trailer, but much of the trailer's weight is a lot lower. Therefore, overall, the trailer and load "feel" stable despite light trailer weight and higher load placement.
In both cases, carrying two sea kayaks is a snap as they are a light load for trailering. Always put boats as close to the center as is practicable, to reduce chance of flipping.
If I needed to carry 4 sea kayaks I would not use the narrower snowmobile trailer, because the added weight would sit near the ends of the crossbars, therefore OUTSIDE the wheel track, which is a precarious position. The kayak trailer supposedly will haul 4 sea kayaks using stackers; however, I personally am setting the limit at 2 sea kayaks to stay well below the load limit of 350 lbs. But even with boats loaded to near the crossbar ends, the weight would not extend outside of the wheels. That's a good thing.
I know you were asking about utility trailers, but the load placement, wheel track, tire width, and center-of-gravity factors will affect your flippiness just as they do with any other kind of trailer.