It appears that anyone can edit my website, why is this?

This is not the case at all.

The reason why you can see the editing facility when viewing your website in your internet browser is simply because you have not logged out of your PromoteMyPlace account before viewing it. However please be assured if anyone else was to enter the URL of your website they would not see the edit function as they are not the account holder. 

Therefore go back into your PromoteMyPlace account and click the 'Logout' button which can be found in the top right hand corner of your screen. 

Then enter the URL of your website once again in your browser and the 'edit' functionality will no longer appear.