The issue is not HP, but RPM. As long as the motor spins at the manufactures recommended RPM, and you didn't change the gear or pulley that drives the lower wheel, it will spin at the same RPM as with the smaller motor. But it will cut more efficiently under load.
Nice looking saw, BTW. I've never heard of Beaver Brand. Is that a throat height extender, or is that simply the way it's made?
Some things I would check before purchase:
Are the wheels coplanar? If they aren't, it will be hard to get the blade to track right. Usually issues of planar-ness (whatever you call that condition) can be fairly easily resolved with shims or even tightening something.
Are the tires in good shape? Changing tires is a serious pain in the butt. It is a straightforward exercise, however, with plenty of YouTube's to get you through it.
Upper and lower blade guides ok? If they are missing or broken, you can hopefully find replacements, but after market options might be viable.
Deformation in the neck, usually from leaving a fully tensioned blade on for too long. This isn't the end of the world, but it will effect blade tensioning, blade length, and even planar-icity :).
Tensioner spring sprung? They wear out over time. You can extend spring life with washers, but eventually you bottom out and can't apply enough tension.