Wow, this is an interesting question and a common concern for employers.
Who hasn’t questioned the “long weekend flu,” or the Monday hangover/headache?
You cannot discipline someone for being ill, but you can discipline an employee for attendance issues. Your first step should be a frank conversation with the employee where you discuss the trends that you are seeing, and what can be done to correct it. Maybe there is something contributing to this trend; could be alcohol or drug addiction, could be that the employee is a weekend caregiver for a sick relative. The point I am trying to make is that sometimes our first instincts are not accurate; what’s more, in our experience, most employees do not keep track of there sick time themselves and are oblivious to the patterns.
Once you have that conversation, you can request doctor’s notes for future sick days, which could also positively change the behavior.
Ultimately, you can discipline for this, but you have to walk that fine line of addressing it as an attendance issue and not some type of misuse of sick time.