How is buoyant force related to weight?

Buoyant force is related to weight, but not to the weight of the object that is experiencing the buoyant force. Buoyant force is equal to the weight of the fluid displaced by the object experiencing a buoyant force.

Note that the word fluid was used above, not water or liquid. Buoyant forces exist whenever an object is immersed, or partially submerged in a fluid. This includes you sitting in the atmosphere right now. There is buoyant force on you equal to the mass of the volume of air that you displace.

Suppose an average person has a mass of 70kg Since people are largely composed of water, which has a density of 1kg/liter, that person has a volume of about 70 liters or ##0.070 m^3##.

We can then multiply that volume of air by the density of air at 1 atmosphere of (about ##1.2 kg/m^3##)to find the mass of the displaced air

0.07m³ x 1.2kg/m³ = 0.084 kg, or 84 grams (between two and three ounces).

A mass of 0.08 kg has a weight of about 0.8 Newtons, and that is the buoyant force from air. So when you stand in air and weigh yourself on a scale, you'll appear to weigh about one cooked hamburger patty less than you actually weigh due to the gravitational force on you alone.