Could someone please name a fatal disease that shows up later in life?

Syphilis -- or, as I like to call it, That Which Used to Keep Men Faithful =)

Damn antibiotics ...

spinocerebellar ataxia. it doesn't kill very quickly, the process is slow. But there are some cases when its a fast process. a girl named Aya Kito, a long time ago had that disease and was diagnosed with it when she was 15, then died at the age of 25. if you watch on youtube, the drama series 1 litre of tears, it might inspire you for your script you're going to write. Its a really good drama.

16 is not considered later in life (in response to you: it's alright....but still not any more likely)

diseases don't show up at that age...

there are diseases that show up around middle age though (Huntington's)

You'd probably want something heriditary.

Heart disease is a silent killer. Most people don't even know they have it.

Breast Cancer? or AIDS last a lifetime too

cancer

meningitis

untreated rabies

Sorry, I don't know if those would work for a play.

aids