  We generalize a special case of a theorem of Proctor on the enumeration of
lozenge tilings of a hexagon with a maximal staircase removed, using Kuo's
graphical condensation method. Additionally, we prove a formula for a weighted
version of the given region. The result also extends work of Ciucu and Fischer.
By applying the factorization theorem of Ciucu, we are also able to generalize
a special case of MacMahon's boxed plane partition formula.
