I do some weights but usually hang board and pulls up after the climbing session. Do you think that it is good after? Also I see some people doing weight training before they climb?
It depends on what your goal is:
If the focus is on building strength in your muscles and tendons to supplement your climbing, then exercises first and climbing second should be the order because you will have full strength to perform the exercises
If the focus is on the climbing and technique then you want climbing first and exercises second as this will give you more reserves of strength for your your climbing and technique.
Additional factors also come into play as whether you tend to fall early on or late into a problem that you are working as this will also guide whether you want to work on strength when you are fresh or fatigued.
It is variable based on your needs and what stage of training cycle you are in.
Hope that helps!