I saw this post in StackOverflow that encouraged me to use Session State in my Azure application.
I followed this post and generated the tables, but my problem is I can't have an additional Database for that, I'd have additional costs too.
My question is: there's a way to make the Session State know that it should run in both tables, even if I don't have a specific connectionString pointing to the database ASPState?
If you need session state then I would recommend skipping the SQLAzure provider and using the AppFabricCacheSessionStoreProvider instead. It is now in production, in some of your links above it wasn't yet. I have found it pretty easy to use but there are additional costs. But if you use SQL Azure you could end up with additional costs pretty soon anyway as the database size grows.
Having said that, I am in the process of eliminating session use in my app on Azure. Make it much easier to add more server with no worries, unless your app has sessions deeply ingrained.