Green’s Dictionary of Slang

1. (orig. US) a hat [20C+ use is Aus.].

1859		Matsell Vocabulum.
1895		C. Crowe Aus. Sl. Dict. 67: Roofer, a hat.
1941		Baker Popular Dict. Aus. Sl. 61: Roofer, a hat.

2. (US Und.) a country gentleman [they have ‘a roof over their head’].

1903

H. Hapgood Autobiog. of a Thief 78: I always travelled with three or four others, and went for gatherings where we would find ‘roofers,’ or country gentleman.

3. a third-rate, run-down theatre.

1923

J. Manchon Le Slang.

4. (US Und.) a tramp who travels on the roofs of passenger carriages.

1916		‘A-No. 1’ Snare of the Road 32: ‘Roofers’ [...] travel lying stretched at length upon the metallic roofs of the coaches.
1931		Irwin Amer. Tramp and Und. Sl. 160: Roofer. – A ‘rambler’ who rides the roofs of trains.
1949		Monteleone Criminal Sl. (rev. edn).