To publish a stand alone table in AGOL I went to the Share tab --> Share As section --> Web layer --> Publish Web Layer. Since it is not possible to publish a table by right clicking on it and Publishing it like you would with other spatial feature layers. Anyways this worked fine.
When making some changes and wanting to overwrite the table feature service, I try Share tab --> Share As section --> Web layer --> Overwrite Web Layer. But then I can't find the table as a Web Feature Layer in my list of content. Is there a way to complete this task?