Green’s Dictionary of Slang

topper n.3

1. [19C] (UK Und.) a hat (but not a ‘top hat’).

2. [early 19C+] a top hat.

3. [late 19C] a cigar or cigarette end.

4. [late 19C–1900s] a tall, thin person.

5. [late 19C–1950s] (usu. US) a loosely cut jacket or coat, generally worn by women and children.