Some of my beets appear to have almost heaved themselves out of the ground. They are about 11/2" in diameter. If I leave them alone, will they continue to grow bigger? Or are they done growing once they have almost come out of the ground on their own?
Most varieties are ready to harvest 60 days from planting.
When to harvest depends many times on personal preference, some people like smaller Beets.
Look for the shoulder of the Beets protrude from the soil line. If the roots are being pushed up further, they may have been more crowded in planting, and I would go ahead and harvest. If much of the Beet is exposed and the weather is generally quite warm this time of year, it can effect your plants.
For future planting, you can thin your plants when the roots are about 1 inch in size. Then the plants to 4 inches between then. This allows your Beets to grow to a nice full size.