Importance of stone, say (6)
I believe the answer is:
weight
I believe this is a double definition.
'importance' is the first definition.
(weight is a kind of importance)
'stone say' is the second definition.
(stone is a kind of weight)
'of' is the link.
(Other definitions for weight that I've seen before include "Heavy load - preponderance" , "Importance, heaviness" , "Avoir-du-pois" , "Gravitational pull" , "Burden" .)