2-3W? That means it's only a 0.5A, right? A lot of devices don't even charge properly off of a 0.5A USB source.
It wasn't until USB 3.0 that the limits were increased. Additionally the Battery Charging spec was re-written to increase limits for charging ports.
If you can plug your device into any single USB jack on a computer (not just ones with a battery icon next to them) and it will charge, it will likely charge with this project.