Can carpal tunnel weakness go all the way up your arm ?

Carpal tunnel: Yes definitely it can make the arm feel weak compared to the normal side

No: true carpal tunnel only effects the muscles of the thenar eminence in the palm. More proximal weakness can be median nerve related but would be a more proximal level of compression such as brachial plexus, nerve roots at cervical spine, or pronator syndrome. Parasthesias or pain can radiate up the arm from carpal tunnel. Seek care for evaluation.

Yes and no: Carpal tunnel typical occurs at wrist level, however that is not the only location that has "median nerve entrapment!" There are other location/condition such as pronator syndrome or anterior interroceous nerve compression, which is a motor branch of median nerve and present as weakness! CTS can be simple most of time but can also be tricky and challenging.