" Available Memory" counter is not available for azure web app
"AVAILABILITY MEMORY" counter is not available for Azure Web App. users are charged for usage of memory, so it doesn't make sense that this counter is not displayed.
Thank you for reaching out. Unless we’re missing something here, there may be a disconnect in the communication. Our shared resources plans (Free and Basic) have memory limits as seen here: https://docs.microsoft.com/en-us/azure/azure-subscription-service-limits#app-service-limits. However, there is no additional charge for the usage as there is a set fee for the plan level and for each additional instance. You may get throttled, depending on the plan you select, until you scale up or out, but there is no additional charge.
In any case, there is a bunch of monitoring available: https://docs.microsoft.com/en-us/azure/app-service-web/web-sites-monitor
Also, you can check in the portal under your web app settings, search for “quotas”, and also check out “Diagnose and solve problems” and hit “metrics per instance (app service plan)” which will show you memory used for the plan.
Sergey Kanzhelev commented
Also, note our blog post about the support center: https://blogs.msdn.microsoft.com/appserviceteam/2017/05/10/supportcenter/