Let’s say we have a person with a mass of 100 kg who can run at 5 m/s.
Now we can make use of Einstein famous equation of E = MC2 :einstein)
When the person is at rest, the total energy of the person is 100 * (3x108)2 or 9x1018 J
When the person is running, their Kinetic energy can be defined as ½mv2
Ke = (½)*(100)* 52
Ke = 1250 J
Therefore the person total energy is (9x1018 + 1250)J
With a little reworking of the equation, we can get Δ m = (Ef – Eo) / (C2)
Δ m = (1250 J / 9x1018 m2/s2)
Therefore Δ m = 1.3888x10-16 kg
This means the person running has gained mass (even if very small) and therefore Weight.