Carry round a little weight (5)

I believe the answer is:

carat

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'little weight' is the definition.
'carat' can be an answer for 'weight' (I've seen this before). I am not sure about the 'little' bit.

'carry round a' is the wordplay.
'carry' becomes 'cart' (carting is a kind of carrying).
'round' indicates putting letters inside.
'cart' enclosing 'a' is 'CARAT'.

Can you help me to learn more?

(Other definitions for carat that I've seen before include "Measure of gold in alloy" , "Gemstone weight unit" , "Measure of weight of diamonds" , "A unit of weight for precious stones" , "Unit of weight for diamonds" .)

I've seen this clue in The Independent.

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