If you're already on a monthly mortgage payment plan with the mortgage lender then there's really no savings in paying the mortgage payment weekly.
However if you want to pay the mortgage payment in weekly payments then that is okay too as long as you get the full months mortgage payment paid so that it is not considered late.
I've heard that paying mortgage payments weekly instead of monthly saves money on interest but in reality there are no savings by setting up weekly mortgage payments vs monthly mortgage payments.
You can just set it up to whenever you can make the mortgage payments and whether that be monthly or weekly is up to you.
I preferred to just pay part of the mortgage payment weekly as I got my paychecks in but you can wait and pay it monthly if you prefer.
The more money though you pay into the mortgage payment each month the more money you'll save on interest and you'll get the home mortgage down faster and have the house payment completely out of the way sooner.
Then when you get the house paid off you can put those mortgage payments into a savings account to earn interest and have a good savings account.