サイズが合うかどうか着てみます。
As I understand it, the "サイズが合うかどうか" part is an embedded question (疑問節) meaning "whether the size fits or not", but I fail to understand how the embedded question is connected to the rest of the sentence.
The following is my analysis:
- I don't think the embedded question is the object of "着て" (with the "を" particle omitted), because you wear clothes, not a question. I think the object of "着る" is implied by the context.
- Maybe it's the topic of the sentence, with "は" particle omitted?