* You treated the system's memory like it was some infinite resource. It's not, you need to make sure your application efficiently handles memory and takes measure to ensure it doesn't grow too large. Would you want it swapping on a regular host?
* You thought you could get away with a free database that is used for development.
You're using an application that isn't built well for shared environments, it expects dedicated hosting.
You'd be better off designing your blog around Azure Web Sites, knowing the advantages and disadvantages of the platform and taking advantage of them. Don't try to shoehorn it in.