Cheese (being cheesy) comes from the phrase "say cheese!" at photo portrait time. It’s smiling, not because you necessarily feel like smiling, but because you want to appear as though you feel like smiling. And it now it represents all those times when someone wants you to feel some emotion (maybe even manipulate you into it) but it doesn’t work.
Haven’t you noticed how that engaged couple is oblivious to cheese? It’s real to them. There’s nothing cheesy about it. But you’re on the outside. It’s a mystery as far as you’re concerned.
The key to avoiding cheese yourself is to make sure you earn it. If something is sad, then give enough details (and do a good enough job at it) that it becomes real to your readers, too.
On the other hand, another excellent trick for handling potential cheese is to state the issue objectively, matter of factly. Just give the facts, and let the reader feel it for herself. This keeps you out of the spotlight in a way. It keeps you from being blamed for trying to create emotions, failing, and ending up with cheese instead.
(*Then again, maybe you’ve just bought too much into the scientific bias. You think you’re a logical being. You don’t let emotions cloud your clear vision of truth and existence. Maybe you’re afraid of your feelings, or at least of letting them show. They’re too personal, and revealing them makes you vulnerable. If you suspect this to be the case, try having some courage, growing up, or whatever it takes to enjoy your emotions a little more.)