Azure Websites Memory Usage For Multiple Websites with same DLLs
Each WebApp is isolated by the app-pool so if you have multiple copies of the same site, even if they are identical, they will all load their own copy of the assembly into memory.
There is also the security sandbox due to the multitenant nature of the service so interning will not work against that.
To monitor memory usage, you can look at the app service plan. Also useful is process explorer (WebApp>tools>process explorer)