Because you are interpreting the English use of the word 'so' in your sentence literally as 'consequently', you are equating that to ので, but the result in your sentence doesn't follow the action/behavior. You can use だから in this sense, but ので doesn't really work this way. It is more logical.
ので shows a natural or expected cause and effect behavior. 'I eat, so I gain weight.'.
のに shows that the effect is not consistent with the cause. 'I eat, but I don't gain weight?'.
A, therefore B (B logically follows from A) = ので
A, and yet B (B does not logically follow from A) = のに
'I'm just always eating so why aren't I fat?' basically says the same thing as 'Even though I'm always eating, why don't I gain weight.' (The result of not gaining weight is not consistent with the action of eating constantly).
Finally, 「なんで太いじゃない??」is incorrect.
「なんで太らないんだろう??」would be best.
An i-adjective + じゃない is like saying, 'It is ____, isn't it.' Remove the final い and replace with く before adding ない (太くない). 太い is, however, used mainly for objects and not people, with 細{ほそ}い being its antonym.
When describing people, however, generally the present-progressive form is used to indicate being overweight or underweight: 太{ふと}っている・太{ふと}っていない // 痩{や}せている・痩{や}せていない.
For people (in the process of) gaining weight or losing weight the plain form is used: 太{ふと}る・太{ふと}らない and 痩{や}せる・痩{や}せない.