Green’s Dictionary of Slang

1. of a jumper, having sleeves that hang loose under the upper arm.

2002		ScreenWriter ‘Rita’s Hair Color’ posting on Coronation Street Message Boards 23 Sept. 🌐 Rita shrugs on her favourite batwing jumper, the one with the nice pearls on the shoulders, and a sensible A-line skirt but them heels are staying.
2003		Chixwear 🌐 ‘Camelia Batwing Sweater’ £60 [...] This is a funky ‘batwing’ shaped jumper has a slashed neck and a hand knitted appliqued camellia flower on the shoulder.

2. thus, of a person’s upper arms, flabby or old so that the skin hangs loose.

2002

‘Drop a dress size for Xmas’ on ThisIsLondon 🌐 To prevent batwing arms: sit astride a bench holding a weight in one hand.