I want to get an adult tricycle because I have balance problems, but I think that a triking/biking would be a good way to help get my weight under control. I weight about 40 pounds more than the advertised weight limit for the trike I can afford. How bad is the risk? I wouldn't be biking too fast. Just a couple miles a day.
Answer: Maybe - speed isn't the problem.
While most "limits" have generous tolerances, your manufacturer's warranty could be unusable if there was a structural problem.
Your brakes would have to dispel more momentum while stopping, so that will increase wear and runout distances.
Riding is a great way to get exercise, and I've successfully ridden road bikes while being at the upper boundary of weight.
Suggestion: can you try a spin bike at a gym? Could give you the cycling motion without needing to be on a bike at all. They are heavy, solid and stable so you're not going to fall off.