Welcome to the forum, @NimaWishing! You may already know this but the difference between "Gluten Free" and "Certified Gluten Free" is the difference between having less than 20 ppm and less than 10 ppm. "Gluten Free" is an FDA standard and "Certified Gluten Free" is a standard of the GFCO, a nongovernmental third party certification organization recognized internationally. 

My daughter is a super sensitive Celiac, and she was just glutened by Ore Ida Tater Tots, which are labeled gluten-free on front of the bag, but not certified on 9/25/24. We will not eat anymore Ore Ida until they are certified.

Weak positive is still a positive test.  This article might be helpful. It breaks down each type of test, and what a positive results means in terms of the probability that you might have celiac disease. Using biopsy results only it does not require Marsh 3 damage to make a diagnosis--a diagnosis can be made with Marsh 2 level damage, especially if you have even a weak positive blood test for celiac disease. Per this article:      

It is also possible that because you have been alternating between being gluten free and not gluten free, the damage to your small bowel villi was less than it might have been had you not been gluten free for extended periods of time. But again, there are other possible causes for villi damage besides celiac disease. I would also inject a corrective here to what others have said about IGA deficiency. IGA deficiency does not guarantee that IGA celiac antibody scores will be negative, it simply increases the likelihood that they will be negative, particularly in those cases where the scores wouldn't have been high anyway or were borderline. In other words, it lowers the scores and pushes them toward the negative end.

I do know that any test using iga is pointless; they don't do them--they only do the igg based tests.  Deamidated gliandin abs igg has never been positive or even close. Marsh has other explanations per tge first GI that saw me and decided that I did not have celiac after all....so with only a marsh 2 and not a marsh 3 and the ttg igg at its highest ever only being labeled "weakly positive" which can be considered normal for some people--he stated that number should be significantly higher to really say celiac -- so it's all confusing.  I dont have additional symptoms that someone else was asking about.