B & S 80202 0413 wont run properly?

I Have the above engine on a merry tiller, I dont know how old it is but it is getting on a bit, I am having some trouble starting it & when decides to start it runs for a short time then cuts out then its back to square one, I have changed the spark plug but it made no difference, I have noticed that on the carb diaphram one of the two small flaps only covers part of the hole, I intend to change this diaphram, but could it be some thing else causing the problem?
Hope you can help.