Green’s Dictionary of Slang

sweetheart v.

1. to make advances to, to ‘chat up’; thus sweethearting n.

[UK]G.A. Sala Twice Round the Clock 220: Sweethearting in cabs and carriages. [Ibid.] 273: Dozens of couples sweethearting.
[UK](con. 1840s–50s) H. Mayhew London Labour and London Poor III 390/1: One of his mates sweethearted the servant, and got her away, and she left the door open.
[UK]M. Davitt Leaves from a Prison Diary I 26: To obtain the requisite knowledge of the interior of a place which is ‘spotted’ for operations, the game of ‘sweethearting the slavey’ is gone through by the best-looking member of the gang.

2. (US black) to have a (sexual) relationship with.

[US]‘Iceberg Slim’ Mama Black Widow 65: Ah wish Ah wuz sweetheartin’ wif a cute rich fella lak thet Grampy.