TLDR a pair of kites flown at different heights would not need an anchor to stay aloft if there is sufficient wind speed difference between the lower and higher kite levels.
This is just for fun/curiosity although it might have some practical applications as small aerostat balloons have.
How it works:
Assume at a 20m height wind blows from east at 3m/s and at 200m altitude it blows from west at same 3m/s. Yeah its implausible to have an 180degree change, but for explaining purpose the point is there-s a 6m/s delta-v aka wind shear between 20 and 200m altitudes. Even greater gradients are found in low jet streams over a ~200-300m altitude difference.
Assume the two kites are anchored at same point and both have the same pull force - the lower kite pulls its line westwards with e.g. 500grams line tension the high kite pulls the same force and same angle eastwards. The horizontal components cancel each other which means the anchor point is pulled vertically, so a simple weight in a nacelle (carrying ballast or payload) with the weight twice the vertical pull of each kite will simply float in the air without a ground anchor.
In actual low level jet streams both low and high altitude winds are (mostly) in the same direction, yet a vertical shear of at least 5m/s is sufficient to keep aloft a decent payload.
An interesting feature of this system is it does not need very strong lines - if wind shear increases the system would just gain altitude until it finds a level where pull force balances the nacelle’s weight.
There-s also potential for steering, e.g. the lower kite can be a two line steerable kite like a NPW and an autopilot within the nacelle could search for the higher delta-v, similarly with a glider seeking thermals except here there are only three choices the stronger gradient is either left or right or the binary kite is already within the strongest stream.
A variant with two lower kites each a couple hundred meters apart (lines drawing an inverted, tilted V) would automatically steer towards the higher delta-V stream.
PS the low kite can be a very light drogue/parachute (made of e.g. garbage bag foi)l while the full lift is provided by the high kite. The whole thing is disposable.