Green’s Dictionary of Slang

to court, to pursue sexually.

1838		Dickens Oliver Twist (1966) 231: Betsy’s a fine girl. Stick up to her, Tom. Stick up to her.
1842		J. Labern ‘I Don’t Like to See’ Comic Songs 10: I don’t like to see [...] a Boy about 12 sticking up to a Gal.
1864, 1867, 1870		Hotten Sl. Dict.
1876		Sheffield Indep. 23 Dec. 15/2: Dick began to make a pretty open brag that Mrs Mahoney was sticking up to him.