Buying everyday things, like groceries, lattes and having your car serviced, centers around your life week to week. Bills are normally scheduled for payment monthly.
When you get paid can be on a very different schedule. Planning your weekly and monthly spending based on when paydays happen, therefore, usually doesn't make sense.
Changing your thinking about paydays is probably the most difficult step in changing your view of your everyday money. It may help to look at the money you receive, regardless of source, generically as income with no dates attached.
When paydays are no longer important to you, you will no longer be living paycheck to paycheck. And what you do with your paychecks becomes very simple.
When paydays are no longer important, you are free to decide when you will give yourself the money that you use for buying things with cash. Since this type of spending is typically centered around your life week to week, giving yourself a weekly allowance makes a great deal of common sense.
When paydays are no longer when you pay bills, you are free to schedule bill payments monthly the same way they are scheduled.
Paying bills once a month is too infrequent. Weekly is not appropriate since weeks and months do not normally start on the same day and the number of weeks in each month varies. The best compromise is paying bills twice a month.