Hi,
Do you know the exact date of death for the person you are looking for? It might mean you need to order a death certificate but its better paying £7.00 than the fee for a grave search.
I have found with both Salford Diocese and Burnley Cemetery that when I emailed them with the exact date of death, they gave me the plot number and there was no question of charges. However without the exact date Salford Diocese quoted £30.00. I must admit that I haven't had any contact with Weaste though. When I have emailed, I never tell them I am researching family history.
Once you've got the plot number its just a matter of obtaining a plan of the cemetery. You should be able to get one fairly easily and if not I am sure there will be one at the entrance to the cemetery.
I am not sure about graves being arranged by year of burial. They are arranged by religion; CofE, RC and Non Conformist and some graveyards have Jewish and Muslim sections. Then I think it would depend if it was a private family grave or a public grave. The public graves might well be arranged in order of burial.
Hope this is helpful.
Luzzu