Yes, and j i = -k, k j = -i, and i k = -j. It’d be nicer if it was commutative, maybe, but then you’d have to give up associativity.
I’m sticking to living in valleys then, if I weigh more when I go uphill.
You’re forgetting that the gravitational field is slightly weaker at greater heights, also, and on the surface of the Earth, this effect more than cancels out the potential energy effect, so you weigh less atop a hill.
But the system of “the Earth and you” will have gained mass! If you used a source of energy outside the system to go up the hill, that is… e.g. hitch a ride in a UFO.