I'd have to see how wide/thick the strip of velcro is, but my experience with vecro is that as long as the glue is properly adhered to the surface, the gripping parts will grip to itself perfectly and hold more than you'd ever imagine! Remember that velcro wall and people would wear "velcro suits" and jump onto the wall? Well, if it could hold a human, fat cats shouldn't be an issue.

Just make sure that you follow the directions for applying the velcro to your windowsill, because if the sill doesn't hold the velcro, then the perch won't hold Ripley.