Very small eye went roving round key US city (5-5)
I believe the answer is:
teeny-weeny
'very small' is the definition.
(I've seen this before)
'eye went roving round key us city' is the wordplay.
'roving' indicates an anagram.
'round' means to look at the middle letters.
'us city' becomes 'ny' (I've seen this in other clues**).
The centre of 'key' is 'e'.
'eye'+'went'='eyewent'
'eyewent' with letters rearranged gives 'teenywe'.
'teenywe'+'e'+'ny'='TEENY-WEENY'
(Other definitions for teeny-weeny that I've seen before include "Minuscule" , "Itsy-bitsy" , "Very small" , "Minute" .)