One View
He realized that the people in Whoville do not need fancy decorations or gifts to celebrate Christmas. Christmas is celebrated in their hearts and their spirit, so the Grinch's heart grew 3 sizes because he understood the true meaning of Christmas. Alternative View The Grinch realized he had something to offer the people of Whoville. He kept the sled from crashing off the mountain, so that he could give the presents to the Whos. This service to Who-kind is the cause of hearts to grow, the more one serves their fellow Whos the larger their heart will grow.
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The Grinch's small heart grew 3 sizes that day.
... the story doesn't really tell us exactly the size of the heart, but we know that it was 3 sizes bigger than it was before.