Legal Requirements for Weekly Offs
As per the law, you are required to pay for weekly offs only when the person has worked for 6 days in a week. Therefore, legally you may be justified in denying the leave to that person.
Company Practices and Employee Satisfaction
However, few companies do that as it will give rise to dissatisfaction or even industrial action, which no one wants. If you are facing a problem with a particular employee who is habitually absent, you need to issue a show-cause notice and initiate a disciplinary inquiry following the rules.
The Sandwich Rule
Most companies also have the sandwich rule, which means if he is absent on Saturday and Monday both, the weekly off in the middle is denied.
But tread carefully as the solution may result in a bigger problem for you.