Your question basically has two parts.
How would something fall up?
There are some theories that particles could exist which are affected inversely by gravity, such that rather than being pulled toward the source of gravity, they are repelled by it. We would not normally be able to find such particles, since 1- they would never be near any normal matter, and 2- the particles could never form a large object together on their own through gravity.
How would a disease cause this?
Since you have specified a disease, I assume that you intend for microbes or parasites to be the cause of the effect. So how about this: a microbe that, when it consumes matter, converts it into this type of theoretical anti-gravity matter. The matter would remain inside the human body, despite being pulled in the opposite direction by gravity. 279
And if the chemical properties of the matter were unchanged by the anti-gravity conversion process, then the body's biological processes would treat it like any other matter. The matter would be combined in with normal matter in your blood and cells, where gravity's effect is overcome by strong atomic forces.
Given that the human body is already under normal gravitic pull and does not fall apart or suffer some sort of circulatory failure, it is fair to assume that having some of the matter in your body pulled in the opposite direction with identical force would not cause your body to fall apart or die immediately.
The greatest danger would be a "head rush" - humans who hang upside down for too long can have blood accumulate in their heads, causing loss of consciousness. But in our case, we only need 50.01% of the body's matter to be converted to anti-gravity matter in order for the person to experience weightlessness similar to zero-G that begins to cause them to rise into the air.
The biggest obstacle here is: how would microbes do this? Changing the physical properties of matter is no small feat, one would expect a facility like the LHC to be required to carry out this process. But much of Science Fiction is playing with "what if the rules were a little different?" scenarios, so if we assume that a microbe can do this, then it could produce the effect you're interested in. 279