I think on a crank drive e mountain bike from a regarded manufacturer like cube there is significant lee way for the weight of the rider and you would be very unlikely to get issues, and the heath benefits and fun would out way the risk.
An e mountain bike is after all designed to take punishment.
For a fit but overweight person riding a bike is an excellent non load bearing form of exercise.
The benefit of getting outside into the fresh air in itself is a great mood enhancer.
I think the cost/benefit ratio might make a good case for them being prescribed on the NHS for overweight people!
I am 100kg plus and ride a hard tail Yamaha Haibike carrying loaded panniers cross country to work and have had no issues with the frame in over 5 years riding and 12,000 miles.
I do ride it fast on down hill tracks and this can include getting off the ground coming of steps to land on the track below the step, so I have not treated mine with kid gloves.
You may need to budget to replace the rear wheel with an after market quality strong one at some point, but on a crank drive that is a simple thing to do.