Final answer:
The condition characterized by redness and distended capillaries caused by a weakening of the capillary walls is called rosacea.
Step-by-step explanation:
Redness and distended capillaries caused by a weakening of the capillary walls are a condition called rosacea. While varicose veins and spider veins are conditions that involve enlarged and twisted veins due to faulty valves, allowing blood to pool, rosacea is specifically related to the small blood vessels on the face. It is a chronic skin condition that typically affects the nose, cheeks, forehead, and chin. To manage rosacea, dermatologists often recommend avoiding triggers that can cause flare-ups, using topical medications, or, in some cases, laser therapy to reduce the visibility of the blood vessels.