All these guys make it sound like there was high science involved. Maybe, maybe not. In some cases, I would bet that the designer intended X engine, built it with X engine, tested it with X engine, and then published that number and the CG range. Anything else is unknown territory for flying characteristics. Now some folks may go over that number and play with things like mount, cowling length, and even ballast to hold empty CG. I even knew one guy who filled his hollow crank end (no governor on his engine) with lead shot and resin - landed after a flight with most of the lead and most of the spinner gone, with the airplane really squirrelly on the way back to the airport. He would have been better served with a longer mount and cowling.
Seriously though, you do not know what parts came in really close to limits and which have a bunch of margin. And every design is likely different. Could be fuselage strength, spin and stall characteristics, ability to lift the nose wheel for takeoff, ability to flare in landing, the list goes on and on if you keep the engine CG in the same place but make it heavier. Even worse if you get it further forward and heavier.
Your challenge in going with a heavier engine is how much do you dare increase the bending moment into the airframe from the combined engine and mount? I will suggest zero is an excellent target. I recommend that a Free Body Diagram be done with the design recommended mount and engine, carefully compute FOS on the bolted joints at the firewall, and then see if you can get the same bending moments from your heavier engine by shortening the mount. For instance if you had a base engine at 185# with its CG 30" forward of the firewall, that is 5550 in-lb. The new engine is 200#, its CG should be about 27.75" forward of the firewall, and the FOS in the bolted joints and fuselage should still be on the safe side. They won't change much this way, but you better have a pretty good idea of what you did to your margins.
If you can maintain moments of the firewall forward stuff, you will only have a few less pounds of payload, but it will otherwise behave like the original. If you have a heavier engine that is longer too, now it can be tough to keep the CG in place without resorting to ballast. That can work, but you had better weigh the bird and make sure it is on for CG. I know of a guy who did all this, did a bunch of calculations but never weighed the airplane - it was tail heavy and the first flight ended in a fatal crash. Do not be that guy.
One other way to go with a water cooled engine that is a few pounds heavy is to go with a belly mounted radiator and maybe oil cooler too. See SDS's website and rv6ejguy's posts on this topic. This may keep the stuff forward of the firewall under control, put the extra few pounds somewhere nearer to the CG, and give you less stuff to make work under the cowl too.
Have fun,
Billski