Quite possibly there's a problem with the scope. One crosshair remaining sharp while the other blurs out sounds fishy to me. Possibly it's not focused right, but I doubt it's your eye. You're shooting with both eyes open, right?
If it is the scope, you may be able to adjust the eyepiece focus so the other crosshair blurs and the previously fuzzy one becomes sharp. There may even be some middle ground where they're both sharp.
Your idea of rotating the scope 90° isn't a bad one. If it's a scope issue, the crosshair that was blurry before should stay that way.
Finally, adjust your eyepiece focus while looking at a blank light colored surface with nothing except the crosshair for your eye to focus on. A clear blue sky works, as does a blank wall with light paint. The more light the better when you do this. It can be three feet in front of you ( wall ) or infinity (sky).
Adjust so both crosshairs are sharp and well defined. You may need to rest your eyes a few times while you do that, and the crosshairs should be immediately sharp when you look through the scope. If it's off a little bit, your eyes will automatically adjust but you'll get eyestrain in a short time because of it.
Get someone else who is familiar with scopes to try yours, see if they have the same problem. They'll need to adjust it for their eyes, once that's done they may have the same results you do.
With my scopes, I find there's usually about a quarter turn of the eyepiece between fuzzy and sharp and fuzzy on the other side.
If you do decide it's a scope problem, hopefully Weaver will repair it for you. I don't know what their warranty is like.