Weight and rate of progress of male fatty tissue (8)
I believe the answer is:
momentum
'weight' is the definition.
(momentum can mean weight or importance)
'male fatty tissue' is the wordplay.
'male' becomes 'm' (common abbreviation).
'fatty tissue' becomes 'omentum' (type of fatty tissue in the body).
'm'+'omentum'='MOMENTUM'
'and rate of progress of' acts as a 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 momentum that I've seen before include "driving power" , "Impulse" , "Forward impetus" , "Impetus gained by a moving object" , "Corbynites" .)