Bolt pattern and shaft size should be compatible. I replaced my 12 horse Tecumseh with an OHV 18 with balance weights and everthing was fine. The frame even had an extra set of holes so the extra width of the balance weight cover could be accomodated. I did find the transmission was not happy with the additional 50% of torque and I swapped it out later.
I think you might have a problem with the clutch set up. It mounts on the engine of the 12hp, and I don't think it will mount on the 16hp. I'm sure you can make it work but it won't be a simple swap.
The trans can handle it just fine. They used that trans on the GT5000 that had 25hp.