It's vs Its

It's fucking confusing. Well, not really, but I keep making mistakes anyhow. /r/ simple way to remember which is which.

The cat's food
The dog's food
Its food. <-- WHERE DID THE APOSTROPHE GO???

Its fat <-- The fat belongs to "it"
It's fat <-- It is obese
Sheila is fat <-- Sheila is obese
Sheila's fat <-- The fat belongs to Sheila
FUCKING PARADOX!!!

Its fat <-- The fat belongs to "it"
Sheila's fat <-- The fat belongs to Sheila

Not complete sentences.

It's fat <-- It is obese
Sheila is fat <-- Sheila is obese

These are complete sentences, although on the level of a three-year-old.  If you are able to come up with examples of full sentences where it is impossible to tell from the context which interpretation to use, you win.