Management say they can no longer guarantee the safety of customers and staff following armed raids at the High Street premises.
Until it closes, a security guard will be on hand at all times while the branch is open.
And the society is planning a full review of security at all its other branches.
The decision was taken after consultation with police after the latest armed raid last month.
On August 27, an armed robber burst into the branch brandishing a shotgun. He demanded cash from two terrified women cashiers and then ran off up Forest Street with a quantity of stolen money.
Two years ago, five youngsters from Weaverham High School helped police apprehend another armed robber, by memorising the number plate of his car.
He threatened staff with a firearm before stealing a quantity of cash.
There are around 2,000 customers of the Weaverham branch, who will be receiving letters in the next few days informing them of the closure.
David Whatmuff, Deputy Chief Executive, said: "We sincerely regret any inconvenience the closure will cause.
"However the safety of our customers and staff is our main concern and we hope that customers will continue to use the society's facilities at other branches nearby in Northwich, Winsford and Frodsham."
The society's Northwich branch was raided the following week. Police believe the same man is responsible for both offences.
He is described as being slim, aged around 25 to 30, around 5ft 11 inches tall with no obvious accent.
When he robbed the Weaverham branch he had a black scarf over his mouth. He was wearing a black baseball cap, a blue hooded jacket and blue jeans.
If you have any information, ring the police on 01606 48000.
Converted for the new archive on 13 March 2001. Some images and formatting may have been lost in the conversion.
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules hereComments are closed on this article