Haven't looked at hippo's answer yet but in the mean while I tried:

#!/usr/bin/perl

use strict;
use warnings;

while( <DATA> ) {
    chomp ;    
    print "$_  ->  " ;
    if (
        m/^\/(?:[^\/]|(?<=\\)\/)+\/$/
    ) {
        print " matched\n" ;
    } else {
        print " not matched\n" ;
    }
}
__DATA__
/aaa/
/\a\a\a\/\b\b\b/
/aaa\/bbb/
/aaa/bbb/
[download]

Output

/aaa/  ->   matched
/\a\a\a\/\b\b\b/  ->   matched
/aaa\/bbb/  ->   matched
/aaa/bbb/  ->   not matched
[download]