The Daily Gazette for Middlesbrough would be a good starting point, although there doesn't seem to be any coverage (via FindMyPast) for the period 1929-1939 1920-1929.
Also try the Northern Echo (although this tends to cover the Darlington area rather than Stockton/Norton) and the Darlington & Stockton Times (same publisher as the Echo).
I've also found articles about my Stockton-based family in smaller papers like the Cleveland Standard and the Stockton Herald.
Begin by searching the name(s) you're interested in using the filters to narrow down by years and publications, but be aware that OCR can be a bit hit & miss so also try searching without full names but with known addresses etc.
The search facility on the British Newspaper Archive tends to be better than via FindMyPast.