Beets: Beets are really a matter of personal preference when it comes to the right size for harvesting. They are ready any time after you see the beets shoulders protruding at the soil line. It usually takes about 2 months after planting before they are fully grown.
Eggplant: Pick when the fruit is no more than 3-5" long or 4" in diameter, and before the skin loses its luster. Slightly immature fruits taste best. The fruits should be firm and shiny. Cut rather than pulling from the plant. It usually takes about 2 ½ months after planting before they are fully grown.