What does 더위잡다 mean?

Today I came across the Chinese character 攀 (반), which means "to climb (by pulling oneself up)." I learned that the Korean meaning is 더위잡다, which made me wonder what "더위" means. I already knew that 더위 means "heat" or "heatstroke," and that 더위먹다 or 더위들다 means "to be affected by heatstroke," but the 더위 in 더위잡다 seems to have nothing to do with heat.

Since 잡다 means "to hold" or "to grip" and 더위잡다 means "to climb by pulling oneself up," I am wondering if 더위 could be a merger of the two words "더 (more)" and "위 (above)." If that is the case, then 더위잡다 would mean "더 위(를) 잡다" ("grab hold higher"), which would be a necessary thing to do if one were climbing a tree or ladder. After all, if someone were climbing, one would have to "grab hold higher" to "pull oneself up" higher. Think about it! What would a Korean father say to his son if he were teaching him how to climb a tree or ladder? "더 위 잡아!"