So lets say that I wanted to set a weekly budget... for instance I want to more closely watch my spending on entertainment and eating out and wanted to budget weekly for like $125 - what's the best way to do that?
In reality or in YNAB?
In YNAB the easiest is probably to set up weekly fun money categories and put $125 in. Depending on your payment schedule you may want week 1, week 2, week 3, week 4 and week 5 categories or you may be able to get away with 'this week' and 'future weeks'. I've certainly seen threads on this for groceries.
Of course, this only works if you are religious about checking how much is in the category before you spend it. If you have problems with that you could take out the $125 in cash at the beginning of each week and when it's gone it's gone or using the same principle load up a particular card. I'd use my Revolut card in the UK if I was trying to achieve this.
Much depends on how often you budget. I'm guessing you're not paid weekly, since that's pretty easy. :) If you're paid bi-weekly, you can use an Entertainment Reserve category for the second $125. Move those funds within the budget to the normal Entertainment category after a week has gone by.
This can actually be automated with recurring net $0 split transactions. Each check you would budget $250 to Entertainment. On the same date the scheduler enters a split with a $125 outflow against Entertainment and a $125 inflow against Entertainment Reserve. One week later, the scheduler enters the reverse of that (inflow Entertainment and outflow the Reserve).
If you budget a monthly amount to the category at one time, the Toolkit Extension provides a Pacing feature to help adjust the burn rate throughout the month. (Not on the mobile, though.)