Cross-Bike for my size / weight
A mountain bike is not going to be inherently stronger. 
If anything a larger frame triangle is stronger.
On a mountain bike you have a long seat post that is a point of failure.  

I don't recall seeing weight limits posted for bikes.

Consider a touring bike as they are designed to handle a load. 
Or an expedition bike. 
I would go with a high quality steel or titanium bike.  

Some wheels will post weight like Stans posts weight for some of the wheels. 

And larger tires do take more weight.  You always see larger tires on touring bikes.  Weight = contact area X psi.  A larger tire generates a larger contact area with less deformation.  A larger tire protects the rims.  The wheel still must bear the weight but the rim is cushioned from that ding associated with pinch flat.       

With light use I suspect those bikes would be OK.

From Trek up to 300 should be OK.
Is there a weight limit for your bikes

If you are targeting 300 lbs then consider some more expensive bikes. Like a Salsa Vaya or even more $ a Moots Routt 45.