Oh man. As you can guess from my profile-picture, I'm a fan of Supergirl. The design was nice and very fitting. Even the weight thing doesn't look that bad, in her redesign. But the idea of it, and the personality/reasoning for it ruined the redesign.
Many people forget that Supergirl, more or less, has identical powers to Superman. That armor wouldn't be necessary, as much as it looks good.
The laser "flaw" could be applied to all DC characters. In fact, most of the "issues" this artist has for Supergirl can be applied to the other heroes. Starfire, for example, has strength close, if not equal, to Kryptonians. Tamaraneans have less protection and clothes, but this is balanced by Tamaraneans getting energy and advantages by solar power. Both Tamaranean genders go by this, like Kryptonians. Yet, like Supergirl, Starfire is redesigned as if only the females of the two alien races are affected.
What's wrong with the hair? With Supergirl's strength, shield, and speed, that wouldn't be something that could get her killed. She's not powerless, or a weakling. She has fought against and with Superman many times, in lots of comics.
You see, the issue with these types of DC Comic redesigns is that the issues are made for
every character. These artists probably did not have the confidence, freedom, or type of body to wear what they wanted, as teenagers, and made OCs that have flaws that would also make them not be able to dress more freely. Most female characters wearing what they want then makes said artists envious of the freedom they see others have, and switch the envy with a solution for everything to be like themselves.