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