Burdened after losing wife, ineffectual character does poorly (7)
I believe the answer is:
imposed
'burdened' is the definition.
(to impose upon someone is to burden them)
'losing wife ineffectual character does poorly' is the wordplay.
'losing' is a deletion indicator.
'wife' becomes 'w'.
'ineffectual character' becomes 'wimp' (a weak or feeble person).
'poorly' indicates anagramming the letters.
'wimp' with 'w' taken away is 'imp'.
'does' with letters rearranged gives 'osed'.
'imp'+'osed'='IMPOSED'
'after' acts as a link.
(Other definitions for imposed that I've seen before include "enforced" , "set as a task" , "Thrust oneself upon" , "Forced to be accepted" .)