Badly in love, is in this state (8)
I believe the answer is:
illinois
'this state' is the definition.
(Illinois is an example)
'badly in love is' is the wordplay.
'badly' becomes 'ill' ('ill' can be adverbial as in 'ill-advised').
'love' becomes 'o' (love means zero in tennis).
'ill'+'in'+'o'+'is'='ILLINOIS'
'in' acts as a link.
(Other definitions for illinois that I've seen before include "US state by L. Michigan" , "Oil is nil, strangely, in this state" , "USstate (Chicago)" , "Springfield is the State capital" , "US state and river" .)