Weights are a good idea. If not heres a few thing you can do. Jogging!
A good routine for Muay Thai is this...
Max rep push ups
Max rep squats (full range of motion)
shadow box for minute
Repeat 5 times.
Do that 3 times a week, not on muay thai day though. Jog 2-3 times a week. Jog slow, if you have trouble with that, walk fast and gradually get up to jogging in a few days or weeks. Everything should be a steady progression.
With push ups do this, say you hit 12 push ups on your first set. the next set do 11 and go down one push up each time.
However, each day you do push ups, add 1 push up to how many you do. So if you do 12 push ups monday on your first set, wednes youll do 13, friday 14. Before you know it, youll hit 50-60 in a row.
Also, if you cant do push ups on the floor, do them inclined on a chair or couch.