Nice DDL Trigger on the create database however you can avoid the cross join to sys.databases by using the following query:

SELECT DATEADD(DD,N,dateadd(dd, 0, DATEDIFF(dd, 0, getdate()))) AS backupdate,

DATENAME(DW,DATEADD(DD,N,dateadd(dd, 0, DATEDIFF(dd, 0, getdate())))) AS Backupweekday

,@DBName

,CASE WHEN N % 14 = 0 THEN 'F' ELSE 'D' END AS backuptype

FROM dbo.Tally AS a

WHERE N < 780

Makes no difference in the long run im just personally a fan of shortening code.

As far as the stored procedure goes, most people around here cringe when they see DECLARE CURSOR however i think those who do will also agree this is one of the few cases where you have to use the cursor. The other thing i may look into is a TRY CATCH block for error handling so if one backup fails it does not take out the rest and you can log the failure into a table or have an email alert generated by using something like sp_send_dbmail. It also looks like you went and read Jeff Moden's article on tally tables, if you did not find it here is the link http://www.sqlservercentral.com/articles/T-SQL/62867/ Its a really good read.

The one thing i would suggest though is to move the backup schedule out of the master database and into a utility or tools database. again personal pet peve of any sort of user generated data in the system databases.