If you're frequently ill, or often under the weather, you're sickly. A sickly child tends to miss a lot of school.
Sickly people aren't in perfect health — they are prone to coming down with illnesses, or they just generally don't feel well. You can also describe someone as appearing sickly, if their faces are pale and unhealthy-looking. This "habitually ailing" meaning dates from the fourteenth century, and for a brief time it was also used to mean "causing illness."