Why does Concorde and many other deltas have their wings bent down?
Concorde's ogee (ogival) wing is a smoothed-out slender double-delta.
Slender wings at high angles of attack produce too much positive rolling moment in a sideslip because of the deep chord, so the tip anhedral reduces that. Another solution gleaned from early slender wing studies is the gull-wing, though structurally it's more difficult (the Boeing SST drawings show a gull-wing).
Slender wings when landing are dominated by ground effect in a favorable way in terms of leveling up and lateral stability; tip anhedral helps bring the wing closer to the ground while keeping the benefits of the long landing gear—avoiding FOD ingestion, and more crucially, takeoff and landing performance, i.e. permitting a higher angle of attack in takeoff and landing than a shorter landing gear would allow.
Slender wings at high angles of attack with anhedral tips move the suction peak inwards, allowing the primary vortex to not migrate too far outward, meaning it will work over a larger surface area and therefore will provide more lift.
The first two points are from a paper by Sir Morien Morgan (the father of Concorde), and the last point is from later research. During Concorde's design, some vortex lift phenomena could not be probed in the wind tunnel because the probes themselves would affect the vortices. In Morien's words, a lot of the design was "patient and often ad hoc work" with literally hundreds of wind tunnel models being tested, for example 370 variants of the leading edge were tested.