One chirping adds some weight to conversation (9)
I believe the answer is:
stonechat
'one chirping' is the definition.
(type of bird which chirps)
'weight to conversation' is the wordplay.
'weight' becomes 'stone' (stone is a kind of weight).
'to conversation' becomes 'chat' (chat is a kind of conversation).
'stone'+'chat'='STONECHAT'
'adds some' is the link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
(Other definitions for stonechat that I've seen before include "Small heathland bird" , "Bird of thrush family" , "singer" , "Heathland songbird" .)