Yes, that is the very definition of positive buoyancy and I'm well aware of the definition. However, my question was what is it exactly that causes you to weigh less than the water you displace? If the persons body is naturally negativity buoyant, and the tank is negatively buoyant, then it can't be their body or the tank that causes it. So then it's just the deflated BCD itself? The hoses? The wetsuit? The salt water? Etc, etc?
What Archer said. If you're wearing a wetsuit, it will probably provide enough buoyancy to get positive, if you ditch enough weight. A dry suit definitely would.
However, the more important thing to know is that, generally, the experienced and knowledgeable divers on here (not that I am one of those, mind you - I've just read this multiple times) say that there is no Recreational diving scenario where you should ever need to ditch weights at all (other than possibly when you're on the surface, to maintain positive buoyancy). If you are weighted properly and have a BC or wing of the right lift capacity, the wing will be able to lift you off the bottom. If you were to have a complete, 100% totally catastrophic failure of your BC or wing, then you should be able to swim yourself up to the surface. That latter depends on the presumption that you are properly weighted. If you are carrying 10 # of weight more than what you actually need, then you might not be able to swim it up and so would need to be able to ditch some.
The idea of being properly weighted, again, for recreational diving, ranges from diving in just a pair of shorts with an AL80 in salt water, to diving in a 7mm suit with a single steel tank in fresh water. With shorts and an AL80, "correct" weighting would yield little or no weights at all - and you should be able to swim that up from any depth. With a 7mm suit and a steel tank, you might have a fair amount of weight on to be able to sink that 7mm suit. And, at depth, the suit will compress, losing buoyancy. At the deepest recreational depths, a thick wetsuit could compress enough to lose somewhere around 75% of its buoyancy. If you're at the start of your dive, your tank is full and so it is the most negative that it's going to be. So, if you had a complete BC or wing failure, at 130' (the max depth for recreational diving), right at the start of your dive, that would be your worst case. At that point, you would be negatively buoyant by the amount your suit compressed plus the weight of the gas in your cylinder (e.g. for an AL80, 5 to 6 pounds). Fortunately, if you had that worst case scenario, there would be a couple of things working in your favor. One, you would not have to swim up very far for your suit to start decompressing and regaining some of its buoyancy. If you were, for example, 20 pounds negative at 130', you would not have to swim that 20 pounds all the way to the surface. Remember, because we're assuming you're correctly weighted, that means when you get to 15', you should be neutral with an almost empty tank and an empty BC. That means, with a full AL80, at 15' you'll only be 5 - 6 # negative. So, in this example, you'll gradually go from 20 # negative to 5 # negative as you swim up.
The problem you always have to keep in mind is if you are correctly weighted and you drop weights when you are 100' down (and wearing a wetsuit that is compressed because of the depth), as you ascend your wetsuit is going to become more positively buoyant and (again, if you were correctly weighted to begin with) you are going to become positively buoyant overall (unless you have a full tank and only ditched 5 or less pounds) and end up corking right to the surface, possibly inducing Decompression Sickness due to a too-rapid ascent.
Also, if that worst case scenario really did come to pass and your BC is completely useless, you can hold down the purge button on your octo to dump air. The more air you dump, the lighter your tank will get, also helping you to swim up. Wasting air in an emergency situation may sound counterintuitive, but the option is still something to keep in mind. EDIT: As a LAST resort!
The next thing working in your favor is that a 100% failure of your BC is pretty darn unlikely (according to what I've read). If it does have a failure, it will most likely still hold some air - just not as much as it's supposed to. So, it will still give you some lift, in most failure scenarios. Especially if you maintain some self-awareness and can orient your body to keep the hole in the BC at the lowest point.
The last thing working in your favor (if you're striving to be a self-sufficient diver) is that you should have a buddy who can help you get to the surface, if your BC really does have a complete failure.