It is not considered 'high priority'. It moves through the system at the same speed as regular first class mail. It is actually delivered at a slower pace because, since signature is required and there is often no one available to sign, attempted delivery notices are left and it can take extra days to actually receive one.
Certified Mail is not delivered on Sunday. Except for the holiday season, when regular Priority Mail packages may see Sunday delivery along with Amazon, the only things delivered Sundays is Amazon, in selected areas of the country, and SOME Express Mail, not all. USPS is now calling Express Mail 'Priority Express', which to me as (now-retired) USPS employee made no sense and just confuses people.