If you have built up a large buffer eg a month's pay, you can afford to just put away a set amount each week for the month's bills. Say, total set bills & outgoings are £2000, you could transfer £500 each week and not think about it ever going short. But when you don't have that buffer you really have to track things for each separate week!
We get paid weekly in this household too, and are on less income + more than 2x your rent, but only 2 children. I found I was chasing my arse with planning for the typical 'monthly' bills. Changed to week by week basis and it worked brilliantly for us. This may be useful for you, or not, but I'll try be clear about what I did:
1- Confirm your total monthly income that goes into your banks, 4 x pay
2- Confirm every single bill plus its date and any regular outgoing - this includes each adult's spending money (honestly, if you're skint this should be zero/minimal or a set amount eg £15 pw). Don't forget debts - if you pay them monthly, divide by 4 and this is a weekly amount included in your list. Yours would be £89 put away each payday.
3- Get a blank calendar month with the numbered days, and note down the date each bill goes out.
Make a list on the side of outgoings that aren't monthly bills, but you'd need to budget for in each week eg the food shop, petrol, 25% of rent.
Any less regular bills eg a quarterly subscription, you note it on the calendar day it would go out but in brackets/different colour. If it's a high amount, see next.
Don’t just rely on your memory, look through your statement for the last 12 weeks to see what you’ve been spending on. Print them out and use highlighters to show bills vs unnecessary spending in your household account.
4- Are there any huge irregular bills like annual car insurance? Figure out how many weeks until next one, divide ££ by weeks and now that is also a new weekly 'bill' you must add to your calendar. If you're lucky you'll have recently paid any big irregular bill, so you'll have a smaller amount to save over more weeks. The money you save for it each week you actually put aside in either a separate account, cash envelope, or a specific pot like the ones on the Monzo app, until it's time to actually pay it.
5- Now: you can look ahead and see how much is going to be needed in a particular week. It won't always be the same. Like you have noticed, the remaining amount will fluctuate, and along with that will be your ability to spend outside of bills or to save, and the risk of going over what you've got for that week will increase/decrease.
6- Let's look at February to use this weekly budget. I have attached example pics of a (very simplified!) 'bill calendar' and the weekly budgets of Feb.
Let’s assume you get paid on Fridays. You check the date of each Friday, that will start the 7-day period you will match on the bills calendar. So for Feb the budgets will be 3rd-9th, 10th-16th, 17th-22nd, 23rd-1stMar.
What bills are going to fall within that particular ‘pay week’?
Add all your weekly outgoings from your list! Total up.
For now, since you are experiencing shortfalls, do not automatically transfer all the leftover money into personal accounts.
Write out the budgets for the next few weeks so you can predict where the future ‘high’ weeks will be, which means needing more leftover money in the account to cover them.
7- Once you can see you have a decent amount left from each week, you can make safe guesses about how much to leave in as bill buffer, and how much to put aside for things like emergency savings, family clothing, presents, etc. Again, best putting these latter ones away separate to your bill account.
IMPORTANT: You and your partner need to be very clear and committed to both keeping the bills account just for these planned outgoings, and for not spending all the week’s leftover money! If you find you can afford it, increase your weekly ‘spending money’, but update your list so it’s always planned and gets spent from your personal accounts.
A big bill buffer that stays in the account means you will be able to just work off a monthly budget and transfer an equal amount each week, knowing that overall everything will go out no problem, no need to write out the next 4, 8 etc weeks!