Objection seen as having little weight (7)
I believe the answer is:
scruple
This might be a double definition.
'objection' is the first definition.
(I've seen this before)
'little weight' is the second definition.
(I've seen this before)
'seen as having' acts as a link.
This may not be right. Some or all of it may belong to one of the definitions.
Can you help me to learn more?
(Other definitions for scruple that I've seen before include "Moral qualm" , "A light-weight" , "Weight (on one's conscience?)" , "Objection" , "carrying little weight" .)