The Schwinn wheel is about a 1/2" larger in diameter than a standard balloon or MTB wheel, so there's no way that the tire could be made to fit. They're simply not interchangeable. This gets a lot of people, but there are probably 5 or 6 different sized wheel standards that could be defined as "26 inch" in some way or another. It just happens that the MTB community adopted the old balloon tire size with 559 mm rim and that has become the modern standard. But the Schwinn middleweight rim is 571 mm.
Bike tire sizing is absurd, generally speaking. If you come into it with assumptions based on how car tires are sized, like I did initially, it'll be confusing as all get out. But the naming convention is based on the outside diameter of the inflated tire, rather than the wheel diameter. Or rather, the perceived outside diameter, because once you put a wider or narrower tire on than what the size was based on (say, a 26 x 2.125), the tire's outside diameter no longer matches the named size. Case in point - a 26 x 1.5, like what's on my touring bike, actually measures out to slightly under 25" overall, even though its called a "26". Now, if the industry is going to standarize based on a wheel size and put different diameter or width tires on it, fine, but they should name it based on the wheel size too. But that isn't what happened.
Enter into this situation Schwinn and the middleweight. What they did, essentially, was to adopt a larger diameter wheel so that when they used a narrower tire, it still inflated up to be approximately 26". Since the tire was narrower, it was also lower profile, so to maintain the OD, the rim had to be larger to make up the difference. It's like plus-1 sizing of car tires, for bikes. Quite logical really, but the naming convention screws it up. OTOH, most other manufacturers retained the old 559 wheel size when they moved into middleweight production, and just put narrower tires on them. So a Schwinn middleweight actually has tires that are 26" in diameter, but a Ross or a Columbia, for example, had basically 25.5" tires. Of course, part of Schwinn's motivation was to make money on the back end by having customers come back to them to buy replacements that fit the proprietary size as well.
Is there a way I can post a spreadsheet? I wrote one a while back that breaks down most of the more common sizes and tell you what the actually tire diameters are.
