I don't think you can get the attachment size directly from the POP server. The MIME headers usually do not contain a "Content-Length" header. The best you can do is use a heuristic, by looking at the total message size, which you can get like this:

my $size = $pop->list( $msgnum );
[download]

In general, that number will be higher than the attachment size, because it's the raw byte size of the complete message: it contains the message headers, any text body, the MIME headers for each attachment, and it's inflated due to the attachment(s) being encoded. You might want to account for that by taking a percentage off. In any case, you can be reasonably certain the attachment(s) will be smaller than $size, which I suppose will work for your purpose.