Generally, one can think of many different forces in daily life (normal, weight, friction, EM force, buoyancy, etc.). I can think of classifying them fundamentally as in each of the 4 major forces/interactions (Strong, electro/weak and gravity). Is buoyancy then fundamentally electromagnetic (maybe due to molecular properties) or gravitational (doesn't it come from a weight differential for water) in origin?
The force you refer to is described by Archimedes' principle:
Archimedes' principle indicates that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces.
The key word here is weight, which is defined by:
$$ W = mg $$
where $m$ is the mass of the fluid displaced and $g$ is the gravitational acceleration.
So the force is due to gravity. In zero-G, e.g. in the International Space Station, there would be no buoyant force.
Having said that, I suppose there are two other factors at work. We can write our equation as:
$$ W = \rho V g $$
where $\rho$ is the density of the fluid and $V$ is the volume displaced. So to get a buoyant force the density of the fluid must be non-zero, and the volume of fluid displaced must be non-zero. So the force relies on the fact that matter has mass, and also that solids and liquids don't interpenetrate. Mass arises from the Higgs' mechanism and the non-interpenetration from the Pauli exclusion principle.
Bouyancy is a 'negative weight', measured relative to the replaced fluid. That is, the actual force a mass gives, is reduced by the fluid (gas or liquid) it displaces, and acts as a weight of (mass - displacement). If the density of the mass is less than the fluid, this is negative, and the thing rises.
But one can always treat the percieved weight = vacuum weight - displaced liquid.
It's also important in really precise measurements of weight, since the density of air is 1.216 g/L.