If you're looking for manga similar to Iguana no Musume, you might like these titles. All recommendations are made by Anime-Planet users like you!
Yucy and Yudy are two conjoined twins who have been together since birth. However, as the nutrients in their bodies distribute unevenly, Yucy is beautiful yet slow-minded while Yudy is intelligent and horrifically ugly. Yudy is torn between her love for her sister and her hate for having to care for Yucy; can the two continue to co-exist?
These two short stories by Moto Hagio have a remarkably similar feel. Both are about a young, intelligent, innocent girl who struggles under too-demanding parents, and a younger sister who is more beautiful and generally much better-liked than she. Although they share a lot of cursory similiarities, the actual stories are different enough so that it never feels like you're retreading old ground. Both are fantastic, and if you liked one, there is no doubt in my mind that you would like the other. (Also, both are FINALLY available in English in the compilation: A Drunken Dream and Other Stories )
Hanshin and Iguana no Musume are both written by the same author and deal with the same subject, which is the life of a smart but ugly girl who doesn't get as much love and attention as her beautiful sister. Those two stories, however, take a different look at the issue, Iguana no Musume focusing mainly on the mother-daughter relationship while Hanshin is more about the two sisters.
Both deal with two sisters, one child being seen as perfect and the other as a disgrace. In the end they find a sense of self worth but at what cost?
Noko appears to be living a great life, she's got a good job and a loving boyfriend, but beneath a thin veneer is a young woman who is struggling with her self-image and self-confidence as she fights to keep her weight down. To Noko, being 5 pounds overweight means being miles away from happiness in her lovelife and in her work-place.
Another emotional manga about a woman/girl with extreme body image issues due to her environment. In The Clothes Named Fat is more realistic, and very bleak, whereas Iguana Girl incorporates some fantasy elements, and isn't completely depressing, but both are very good.