Why do legs swell with dvt?

Blood clot: Impedes venous return.

Venous obstruction: The deep veins are major outflow from the legs. When they clot, the blood pools and causes edema by fluid extravasation.

Reason for swelling: The swelling results if the veins in your legs have a significant enough of a blood clot to prevent blood from returning to your heart quickly enough. This will result in increased amount of blood pooling in your leg resulting in swelling.

IT's the blood.: A DVT is a clot in one of the major veins of the leg. This blockages prevents blood from leaving the leg once it enters via the arteries. The pressure within the blocked vein allows fluid to then extrude into the leg itself, causing swelling. It's akin to a clogged drain where fluid builds up behind the blockage.