Climb a weighing device (5)
I believe the answer is:
scale
This could be a double definition.
'climb a weighing' is the first definition.
'scale' can be an answer for 'climb' (scaling is a kind of climbing). I am not sure about the 'a weighing' bit.
'device' is the second definition.
(scale is a kind of device)
(Other definitions for scale that I've seen before include "Plate protecting the skin of fish and reptiles" , "Notes < magnitude" , "Group of notes in ascending or descending order" , "Relative extent as of laces" , "Graduated table" .)