When we discuss weekly wages, we mean two things: (1) salaries being paid once a week, and (2) salaries calculated by weeks. 

First is obvious, you’ve decided to pay to your employees once a week instead of once a month either because the line of work is temporary or the next week you may not need those people or its customary either in your country or in your line of business to pay your employees once a week. Either way you’ve decided to pay once a week and that’s that. The only upside to this is that instead of having to calculate the amounts to be paid and taxes once a month, you now have to do it 4-5 times a month.

However what if you pay by the week once a month. Say that you’ve got people working on ships for solid 6 weeks in a row. This is one example I would consider paying by the week instead of a month. They’re working for you 6 weeks and then they get say the same 6 weeks off. You cannot pay them monthly salary since you don’t know if they come back next time and more so, they may come in the middle of a month and finish at the end of the next month – would they then get two salaries, one at the end of the first month and the other at the end of the next?

Weekly wages are more common in line of work which are not so continuous and are more temporary in the sense. You calculate the monthly salary to weeks and pay a full amount if a full week is covered by the employee.