One of the worst things to believe about writing tragedies is that every scene must be tragic. Filling a serious book with heavy scenes and bleak dialogue will not get you very far. You want to be taken seriously as a writer of Important Things, and so you take yourself and your story seriously, too.
This can be a huge detriment to the quality of your story. When you're working with heavy themes, the most important thing to remember is that to your characters, there is no overarching theme. There are the present circumstances and what they're doing about them, nothing else.
The point is this: sometimes you need humor where humor doesn't seem to belong. You need it in stories about fighting other children to the death on national television. You need it in stories about cancer. And most likely, you need it in your own story, too.
Most people, and therefore most characters, have a go-to type of humor, be it so-unfunny-they're-funny (a la Ross Geller), sarcastic, hyperbolic, or a number of other things. Tragedy, especially tragedy that hasn't happened yet, doesn't change that.
If you have a character who seeks refuge through humor, it doesn't matter whether he's about to lose his eyesight to cancer and the girlfriend he loves just broke up with him and all his other friends are terminal, too. He's going to continue to seek refuge through humor.
Even if your story ends in a way that makes Romeo and Juliet seem happy, just because your book is sad, doesn't mean it has to read like it's sad. Your characters don't know the fate that awaits them. Give them some hope. Let them make inopportune jokes and feel terrible about it afterwards. Let them have a moment of refuge in the midst of their lives falling apart when they have semi-normal banter with a stranger on a bus.
Trust me, your readers will want a break from the heart-wrenching, anyway. There's nothing like the cognitive dissonance of wiping sad tears from your eyes while laughing at something funny that someone just said. You feel terrible for laughing when the situation is so bleak, and yet you can't help it; it's funny. That sort of cognitive dissonance permeates real life, and it will bring that realism into the world of your story.