Obviously it depends on the specific boat, as well as how much weight you're talking about, but in general the following will hold true for any boat:

Front-Rear Weight Distribution
More weight in the rear of the boat leads to a taller, shorter wake with more push. That's why we always start with weight in the rear of the boat.
More weight in the front of the boat gives you a longer pocket, but will remove some of the height and push. The longer the wake the better, so get as much weight forward in the boat as you can without removing too much push.

Side-to-Side Weight Distribution
More weight on the surf side will clean that face up, which is why we load the surf side of the boat more than the non-surf side. As you continue adding weight to the surf side you'll get a steeper face.
Weight on the non-surf side has the opposite effect on the wake.

The important thing to keep in mind here is any time we add weight to the boat that will increase the displacement of the hull, which will make the wake bigger, but where/ that weight is placed will impact the shape of the wake, and shape and size combined are what determines the quality of the wake.

So the answer to your original question is, try putting some weight on the non-surf side and see what happens. If you have enough weight on the surf side you'll see a bigger wake (with possibly a slightly less steep face), but the it will still be nice and clean. If you don't have enough weight on the surf side, the wake will get washy and the quality will suffer, which means that for your specific configuration, you shouldn't run any weight on the non-surf side.