Q:

Why does the Comet's horizontal stabilizer have so much dihedral?

The Comet's horizontal tail has a noticeably extreme amount of dihedral compared to that of, say, a 707:

(Image by MilborneOne at Wikimedia Commons.)
Note how the Comet's tail has about twice as much dihedral as that of the 707 in the background, especially considering the Comet's quite low wing dihedral.
Why such a large amount of dihedral on the Comet's tail?  Does this have anything to do with the Comet's tail being unswept (whereas most later jetliners have horizontal stabilizers that have almost as much sweep as the wings, if not more)?

A:

As mentioned in this question, the two major factors are:

Lifting the tail plane out of the jet efflux area. Placement of the stabiliser root is structurally optimal when at fuselage mid, dihedral can then lift the surface out of the efflux stream. Note that the Comet has a relatively straight aft fuselage cone, which is better for low drag. And like @DaveGremlin mentions in his comment: the jet engines on the Comet are higher than those of the B707 and need to be lifted up higher. 
Reducing sudden main wing wake effects: with a pronounced dihedral, there is always some of the tailplane sticking out into a less affected streamline.

The tailplane dihedral does contribute to roll stability, like main wing dihedral does as mentioned in this answer.

