답답하다 has two meanings so that there are two origins (cf. First
one may be in droooze's link)
1) There is no way to proceed :
There is a vocabulary "첩첩산중", whose meaning is 답답한 상태(no way out of
it). But the direct translation is "surrounded by many mountains".
In ancestor-language of Korean, a mountain is "thaba" so that its
pronunciation is changed into 답.
2) It describes "state surrounded by things" :
When we wear a swimming uniform, then the suit gets stuck to (들러
붙다) our body so that we are stuffy (답답한)
Here pronunciation of 들러 붙다 is changed into 답답 하다.