Has it ever happened?.
Would you know where to start or what to do or if it has ever happened?.
I assume you mean a driver has taken a vehicle through a weight limit unlawfully and now wishes to appeal against it ?
No they are thinking of putting one on a road near me and I want to appeal.
jammymutt:
No they are thinking of putting one on a road near me and I want to appeal.
I would imagine there is a local council procedure to do so - try contacting your local council highways dept 
I’ve no idea but presumably the highways department of your local authority should be able to tell you.
Whether they want to or not 
edit:
Obviously I was too slow again ^ ^ ^ 
Round here they put a notification in the local paper with an address to write with objections, may be worth looking in your local rag 
We had one put in force two years ago on our local high street, despite many objections to the local council, it came in as a 6 month trial, but is still there, and adds 4 miles to my journey each time I come home, which is normally after midnight.
They also try to appear as a green MBC?
Is it me??
Get that grey spray paint and cover the signs with it