Under section 113 of the Aviation and Transportation Security Act (ATSA), "Training providers subject to regulation by the FAA are prohibited from training aliens in the operation of aircraft with a max TO weight of 12,500 lbs".This program is called the Flight Training Candidates Checks Program(FTCCP) and is intended to weed out Alien terrorist's pilot types who wish to operate aircraft in the US. Aliens can be processed quickly by the "expedited processing" system through your Training Provider and the local FSDO only if you are current and qualified on aircraft over 12,500 lbs TO wt. If you want more info on this subject go to
https://www.flightschoolcandidates.gov/. 