An employee abusing sick leave is obviously an annoyance, but it also has many other toxic effects on the rest of your team. For example:
- Other employees start to wonder why they aren't getting more time off
- Other employees resent that employee for not being a team player
- Other employees resent you for letting him get away with the abuse
One of the typical mistakes that managers make is letting the "star" of their team get away with things that they shouldn't. Whether the manager doesn't want to make the star unhappy, or whether the manager feels powerless to actually control the star, it always leads to an unhappy ending.
As you consider how to bring up this issue, you should consider your other employees as well. As a personal example:
I was one of several interns at a software company this summer, and one of the other interns on the team was constantly late and missing meetings. On top of all that, he was getting paid more than the rest of us. This caused some grumblings but we mostly kept it to ourselves.
One day, I was meeting with our manager one-on-one and she brought up the situation, asked how I felt about it and how I thought she should handle it. It caught me by surprise, but she assured me that I wasn't "tattling" on him, she just wanted to hear how I felt about it and what I thought she should do. She met with most of us and had similar conversations, and at the end of the week, it was decided that the "star" was going to be let go.
Obviously, we were interns so it wasn't like any of us had a HUGE impact on the company (ie, we were all expendable) but I thought the way that our manager handled the situation was excellent. It restored team unity and destroyed all of the toxicity and resentment that had been building.
I think your next step should be to talk about the situation one-on-one with other members of his team to gather sentiment. This isn't a situation that only affects you and him. Ultimately whatever you decide should be for the benefit of the entire team, so it's important to see how they feel.
If you find out his teammates are very frustrated by what he's doing, then he's having a negative effect on everyone and should probably be let go. If others don't seem to mind or notice, then you might want to take the issue up with him more privately.
Either way, don't make it an issue of what he should or shouldn't be doing, talk to him about how he's affecting the entire team. That should get through to him, and also restore confidence in you amongst your other employees.