Tire and Rim sizes

[CharleyFarley]

I was looking into wheels, just for the heck of it, and something is confusing me.

I have a cruiser. The tires are 26" x 2.125" (57 x 559)

The rim is 1.25".

Cruiser wheels, online, are 1.75"

The difference between a 1.75" cruiser rim, and the 1.25" rims I have, is approximately half-inch.

I bought the bike, new, from a bike shop, and bought white wall cruiser tires for it. It had wide tires on it but I sold them and don't know what the size was. It seems to me that the 2.125" tires are too wide for the 1.25" rims. I've not had any trouble with this setup but am concerned.

I need to know if this setup is acceptable or likely to fail. I would not be very happy if I had to buy new wheels or narrower tires.

EDIT: It doesn't matter, now. I figured things out. The Electra bike company cheaped out by putting non-cruiser wheels on the cruiser. They were 1.25" and then put plus sized tires on them: 1.75". When I bought white wall tires for it, I got 2.125" thinking I was just going to a plus size, but the original tires were already plus size, which means I've now got plus PLUS sized tires. I never thought to look at the rim size when I first bought the white wall tires.

So, thinking I'd put wider wheels on the bike, I later realized it would cause a problem with the rim brakes. Now I've ordered 1.75" tires. I don't mind the balloon look but they could be a problem especially if the front one was to suddenly split.