Overnight travelers can use Night Tube services on the Piccadilly line on weekends

https://www.scribd.com/document/1074920514/Getting-to-Heathrow-from-Gatwick-Easiest-Inter-Airport-Transfers-178501

Overnight travelers can use Night Tube services on the Piccadilly line on weekends, or consider night buses that connect to Heathrow’s central bus station.