Regions That Share Rows
When two regions both lie inside the same two rows, those two rows give their two stars to them, and every other cell of the two rows is empty. Spotting such a pair is the key move of the Medium grids, and it works the same with columns.
Cells That Crowd a Region Out
Some cells can be ruled out without placing anything: a cell that borders all the cells of a small region would leave that region empty if it took a star. With three cells bent into an L, the fourth cell of the 2x2 square they occupy is such a cell, and stays empty.
A Grid for Each Day
The 6x6 grids hold enough regions for real deductions while staying easy to read. Print one level a day and move up when the grids stop needing hesitation.