No you shouldn't be weight training. Muay thai fighters need quick muscles to move fast, not big ones. This will also cause some stiffening of your muscles and body, and slow you down. Rather than weight training I would be running a lot, 4-6 kms a day if you can.
As far as how often to train, the professionals here in Thailand train 2-3 hours a day, twice a day, but obviously that is something you will have to work up to and not try and do straight away. Good luck and train hard.