on a 1,85 rim, you can fit a 4.00 or 4,10 without problems, if that fits the forks and brakes etc. I have this on the rear rim of my CB350F.
Rather go for a 4,00 instead of a 4,10 if you want the classic "fat" balloon look. The width is the same, but the 4,10 is a 80 or 90% height. Logically, I would assume riding quality will be compromised more if you have more balloon between you and the road... For racing (which I doubt you would do with a brat style) probably this whole fat tyre idea is less optimal..
See size chart of Heidenau for instance:
http://heidenautires.com/tirepress/wp-content/uploads/2015/02/heidenau-tires-spec-sheet-2015.pdf If you can find a 2,15 rim and put that on your stock rear hub with new spokes, it would be a nice low budget solution to allow for a wider rear tyre, if that will clear the chain etc..