Database going over with every post

I am running the latest version of WP. Everytime I post or update, my database jumps from 42 mb to about 76 mb which is over quota. I am only doing posts which would not even use a mb of data. My hosting company has recently migrated to a new server. They are claiming that the responsibility is not on their end and have said that it must be due to a faulty script. I was running 3.5 before, have recently updated and I am still having this problem I did not have this issue before the migration. They are insisting that it must be due to a faulty script trying to insert a large file into wp-post. I don’t know much script, but really need some help with this. I have tried updating, as I said before. but it is still doing it.