I grew up in MI. Mid to late May weather typically will see highs in the 60* to 70* range, with lows in the 40s. Occasionally, days can be warmer (even 80s) or cooler and nights can even have a freeze that late in the year. Plenty of spring rains, perhaps every second or third day on average, so you'd see some overcast days, but it doesn't rain all the time. Overall it's good weather for sightseeing, camping and traveling. Take a variety of clothing, from winter coats to summer shorts. Heck, I pack a good coat when I visit there in June!
Here is a view of 2015 weather along the Lake Michigan shoreline, including daily averages.
Weather Underground: May 2015 in Traverse City MIThe exception will be near the Superior shoreline in the U.P., where the big lake reduces temps and snow remains very possible (though not terribly common) in late May. While I'd usually recommend the boat ride along Pictured Rocks shoreline, I think you'll be too early for that. A brief drive to Tahquemenon Falls (which will be roaring with water) and Whitefish Point (small lighthouse/museum) would still be fun. But for the most part, best to stay along the southern shoreline of the U.P. In addition to the Mackinaw area with its historic forts and massive bridge, you can see the incredibly clear water of the Big Spring at Palms Book SP, the historic buildings at Fayette SP, and many nice views of the big lake along the drive. Farther west, try to visit Bond Falls near Paulding; I like it even better than Tahquamenon, but others may differ.
If you have a thing for lighthouses, the western L.P. shoreline is a treasure trove. The lighthouses are numerous and most are very easy to reach. My favorite is Little Sable Light, at the south end of Silver Lake SP. The light at Ludington is a walk of about a mile and a quarter along an easy trail, if you want to stretch your legs. Sleeping Bear dunes is well worth a visit, and Charlevoix is a nice town to stop and walk around the shops. Drive the Tunnel of Trees route from Harbor Springs to Cross Village. More lighthouses west of Mackinaw City, one at the SP and another one just a couple miles west of town. When in town I always hit the local bakery for some fresh, homestyle cinnamon bread, and their pecan rolls are great also. Dine on whitefish or a pasty (similar to a pot pie) while in the region.