My 9-month-old was diagnosed with eczema at 3 months. She is in the 10th percentile range for weight. Her eczema seems to be worse with wheat or dairy and celiac has been mentioned. Is there an association between low weight and celiac or eczema? Also, what is the best formula for her? Can I stop formula altogether?

There are many types of food intolerances, and some of them can trigger eczema and cause poor weight gain. Low weight gain is a classic symptom.
Apart from celiac, both wheat and dairy commonly cause allergies and worsening eczema in babies, and many of those who are allergic to dairy are also allergic to soy.
It is much more difficult to be allergic to one of the protein hydrolysate formulas, such as Nutramigen. Some kids with severe allergies need to be on an even more elemental formula, such as Neocate, but you will want to work with your pediatrician before making that choice. Your baby needs a good source of protein, calories, fat, and other nutrients. At that age, formula is usually the best way to get these things.
There is now a blood test for diagnosing celiac, called the serum IgA-endomysial antibody test. It is possible that this condition or eczema could be linked to low weight gain, but keep in mind that 10 percent of healthy kids are at the 10th percentile so it could also be the size she is built to be.