I would say "mahina"
Ang kanyang mukha ay katulad ng sa isang bata at mahinang paslit.
vulnerable - be easily prone to something like [madaling magkasakit /madaling masaktan/ madaling matukso]
In the context you have given, you are using the nuance of guilelessness in reference to vulnerability. Indeed, mahina (weak) is a valid equivalent of vulnerable but it seems that is not what you are trying to convey given your sample text.
Instead it seems you wish to emphasize the nuance of childlike innocence when you use the word vulnerable. Thus, I would suggest Mukha siyang bata at inosente OR Mukha siyang batang inosente.
If you did mean to say vulnerable in the sense of helplessness ("he looks young and helpless") then you could use walang kalaban-laban (Mukha siyang batang walang kalaban-laban).