Let me help with this part, but I need to explain what is really going on at each step:
"2nd week I manually had to to the Create Custom payments screen"
Which is what you use to Pay that to the brokerage. This is the function that you had to use because the Liability wasn't "Scheduled." Scheduled = a Helper tool to show you how much you owe and for which Period (paycheck date-based) and how much has been accrued for you to Pay out that tax or other liability.
"and adjust the amount to come out."
This is Not the function that controls Paycheck Deductions. It's the function for you Sending on the deducted funds to the Brokerage. You would select both the employee and the employer deducted balances here, for Paying that out to the vendor name. So, this didn't do what you thought you were doing.
The Amounts are set either on the Edit Payroll item. Or, when something Varies, you do not set it on the Edit Payroll Item. You assign the item to each Edit Employee Payroll setup and set that person's own rate and/or limit, here. Now it is Used in the paycheck computation, and the Pay Check Details is where you see and control the Amounts. This is the step that results in the Deduction and the Match being accrued into a Liability to be paid later, by you, to the brokerage.
"it is currently set up Employee weekly on Friday and Co. match weekly on Friday"
It is set for Pay Date. If you pay Friday, then it is on those paychecks.
"but doesn't show up in payroll liabilities screen, unless I do it manually."
Remember, this is Your Payment to the Broker; not the date of Payroll but the date you Pay what you owe to the Broker, FUTA, FICA, the State. You "Schedule" a Liablity to have the QB program help you stay on track with Paying the Liability on time. Some Federal taxes are owed monthly or weekly or, as with FUTA, annually unless you reach $500 sooner.
And then you have the function of Payroll Schedules, which = these Salary people get paid Monthly, for the dates of 1st-end of the Prior month; this other Subset gets paid Weekly, they are Hourly, and the Paydate is every Monday for the Previous Monday - Sunday as their Work Week.
"or do I have to manually make this entry each week?"
I think you have been confused over what each Function is doing for you. Here is the overview:
Set up Payroll Items to do what you need.
Assign them to the employees to whom that applies.
Pay taxes and other Liabilities on time using the Pay Liability Functions, because you accrued this through Payroll Functions.