I do not want payroll unless I have other work, so I have fairly high fees. Minimum of $150/mo, but $25 per check, $40 for payroll tax payments, $150 for Q1-Q3 payroll reports, $175 plus costs for Q4 reporting. Anything outside of those specified fees is $150/hr. I also charge $150/year for payroll software.
So, for your client example: 3 checks per week, I assume monthly payroll liability deposits = 12 checks per month + $40 for liability payments = $340/mo on average, with some months being $500+.