Small bank carrying little weight (7)
I believe the answer is:
slender
'small' is the definition.
('slender' can be similar in meaning to 'small')
I can't explain the rest of the clue.
Can you help me to learn more?
(Other definitions for slender that I've seen before include "Meagre" , "Faint" , "Gracefully slim" , "associated with 7 [MEANS] suggests modest income" , "Willowy" .)