We study the weight part of (a generalisation of) Serre's conjecture for mod
l Galois representations associated to automorphic representations on rank two
unitary groups for odd primes l. We propose a conjectural set of Serre weights,
agreeing with all conjectures in the literature, and under a mild assumption on
the image of the mod l Galois representation we are able to show that any
modular representation is modular of each conjectured weight. We make no
assumptions on the ramification or inertial degrees of l. Our main innovation
is to make use of the lifting techniques introduced in our recent papers.Comment: 43 page