There is a Parking Control Zone in Weston-super-Mare town centre and Parking Fees apply within the affected region. Roadside parking fees also apply on Knightstone Causeway and Marine Parade. The following sketch indicates the roads likely to be affected by parking charges.
Note This is only a sketch map, consult N-Somerset.gov.uk for accurate details and current charges. In order to simplify the outline, I have included some roads which do not have any "normal" parking provision.
 

 
It is important to check the car-park terms and conditions prior to leaving your vehicle. Whilst some car-parks may be free (conditions may apply) others are chargeable. Many of the supermarket car-parks allow "time-limited" free parking (typically 2 hours.) This list is incomplete, please let me know about any other parking locations.
 
Asda Phillips Road, Winterstoke Road
Ashcombe Park Ashcombe Park Road
Beach (Clifton Sands) Marine Parade
Beach (Royal Sands) Marine Parade
Beach (Uphill Sands) Links Road Uphil
Carlton Street Multi Storey Car Park Carlton Street
Coleridge 219 Coleridge Road
Coniston Crescent Coniston Crescent
Coronation Cottages Column Lane
Flowedown Aisecome Way
Grove Park Grove Road
Hampton Raglan Place
Hill Road Hill Road East, Worle
Knightstone Causeway Knightstone Causeway
Locking Road Car Park - Short Stay Francis Fox Road
Madeira Road South Road
Marine Parade Marine Parade
Melrose 30 Knightstone Road,
Morrisons Elmham Way, Worle
NCP High Street, 4a High Street
Oldmixon (Aller Parade) Winterstoke Road
Oldmixon (Industrial Estate) Oldmixon Crescent
Rear of Station Rear, Station Approach
Sand Bay (Beach Road) Beach Road, Kewstoke
Sand Bay (Bus Terminal) Beach Road, Sand Bay
Sovereign Shopping Centre High Street
Tesco Station Road
The Campus Highlands Lane, Locking Castle
Uphill Way Uphill Way, Uphill
Waitrose 2 Phillips Road
Walliscote Grove East Walliscote Grove Road
Weston General Hospital. Grange Road, Uphill
Weston Milton Station Saville Road, Milton
Worle Parkway Station Diamond Batch, Worle
Worle 58 New Bristol Road