There are only a few limited situations where 'big' could mean 'important', instead of 'fat', and the only example I can think of is 'big boss'.
'Big cop' would always mean physically large to me. Not necessarily fat - possibly very tall and solid. But still physically large. And similarly with 'small' - that would almost always mean physically small.
Why do you particularly want to use 'big', given that it is not an appropriate word in that context?