Westminster City council has published a report looking at how councils can link benefit payments to claimants' lifestyles.
It describes how some local authorities have begun allowing GPs to prescribe leisure activities like swimming and fitness classes.
It is hoped that by using technology such as smart cards, the use of leisure facilities can be monitored leading to housing and council benefit payouts being cut for those not attempting to lose weight.
The document, written with the think-tank the Local Government Information Unit (LGiU), states: "Where an exercise package is prescribed to a resident, housing and council tax benefit payments could be varied to reward or incentivise residents."
Obesity costs the NHS £5.1bn a year and the number of Britons who are overweight is expected to increase by 10% over the next decade.
In recent years the responsibility for tackling public health has moved back to local government, despite many councils experiencing funding cuts.
Councillor Philippa Roe, Leader of Westminster City Council, said: "Councils have a great opportunity to improve lives by thinking how public health can be integrated into existing local services, this can lead to savings being shared across the entire public sector.
"This report contains exactly the sort of bright, forward-thinking and radical ideas that need to be looked at."