You don't clearly state what the problem is. There's tiny chance you can work around the problem. Would buy quality rails though, even if you get the cheap ones working there could be problem with zero retention etc.
Picatinny rail has a spec, but even known big name manufacturers are seldom abiding to it. That usually doesn't cause a problem, unless you're using QD mount on several different rails. Or a non-adjustable QD mount that conforms to the spec. In these cases problem is, the QD mount is too loose or tight in one rail or several.
Weaver doesn't have a generally accepted spec. Usual problem is, it has narrower grooves for recoil lug and picatinny mounts won't fit. Or there are only few grooves and you cannot place the mount / rings where you want based on the scope tube length, eye relief etc.
Chinese crap can be
The picatinny rail tightened onto the dovetail no bother - the QRW base when tightened onto the picatinny is still loose . As there is no recoil from a .22 or an air rifle I wasn’t going to spend a fortune on a picatinny as I thought there’s no need and a lot of the picatinny rails were around the same price . I’ve bought Chinese crap as you say but didn’t ever think there would be that much of a difference .
I thought they were all the same and when I looked for a wider picatinny there all 21mm . 
