Question

Why is Katniss willing to have her name entered into the reaping extra times in exchange for tesserae?

Answer 1

It will get her family food so they can survive and she cares a lot for her family especially her younger sister Prim.

Answer 2

Katniss is willing to have her name entered multiple times for the reaping because she cares about her family, mostly her sister Primrose. She would rather take the risk of taking part in the hunger games herself rather than her little sister taking part in it.