Easing the restrictions on the A985 will also mean the route will be open to commercial vans around the clock from Monday.
Restrictions to the priority route will be lifted completely on 23 December.
The Forth Road Bridge will be closed until the new year.
The bridge was shut completely on 4 December after a crack in a truss end link member at the North Tower.
A travel plan was put in place which involved a priority corridor being set aside for public transport and HGVs between Cairneyhill and Longannet, close to the Kincardine Bridge.
Transport Minister Derek Mackay has now said that commercial light vehicles will be able to use the A985 route.
The priority route will be open to all traffic at weekends, starting from 20:00 on Friday 11 December.
Holiday period
Mr Mackay said: "Clearly the closure of the bridge has had a significant impact, particularly on small and medium sized businesses, and we and our transport partners have been listening to business community views since the travel plan was implemented.
"To address their feedback, from this Monday all commercial light goods vehicles will be allowed 24 hour a day access to the A985 priority route.
"We have also responded to community needs, and so can confirm that all vehicles will have access to the priority route at weekends and outside peak periods on weekdays.
"We also intend to lift restrictions on the priority route completely on the 23rd of this month to coincide with the start of the holiday period."
Andy Willox, Federation of Small Businesses in Scotland's policy convener, said: "We're delighted that the government has listened to the FSB and accepted the vital role our members play in keeping Scotland's economy moving.
"By allowing vans and other light goods vehicles to use the priority route, more essential journeys can be completed is less time.
"Tradesmen with deadlines to meet, wholesalers with shops to supply and couriers with customers' Christmas presents to deliver will be spending more time doing business and less time stuck in traffic."
Restrictions on a priority route for HGVs and buses put in place following the closure of the Forth Road Bridge, are being eased to allow car drivers to use it at weekends.