7 weeks old? it looks lots younger. the dirt you are using looks like dirt, not soil, lol. try transplanting with some potting soil (or better if you can, but the way she looks, im guessing you dont want to invest a lot). are you putting her in a window sill? or taking her outside?
good luck! might try again with some better equipment, you will want to do it again, it is addictive to grow! lol