She wanted to reach out to her sister and let her know she was there for her, but she couldn’t. Entering her into this contest was the closest she could come to show her support, and if Jess won, it really wouldn’t look like she was supporting her at all. Admittedly, it would seem kind of strange changing her older sister’s diapers, but Liz deeply and sincerely cared about her sister, and would rather have this diaper thing out in the open than have Jess try and hide something from the people who cared about her most, especially considering they already knew.
When she went to the store to fill out the contest entry form for Jess, she picked up a brochure explaining what the prizes were and more about the Pampers Princess line.