Jan 10 (Reuters) - The Baltic Exchange"s dry bulk sea freight index (.BADI) fell to a more than two-week low on Monday, as a decline in smaller vessel rates eclipsed gains in the capesize segment. * The overall index, which factors in rates for capesize, panamax and supramax vessels, fell 12 points, or 0.5%, to 2,277, its lowest since Dec. 24. * The capesize index (.BACI) rose 122 points, or 5%, to 2,554. * Average daily earnings for capesizes, which transport 150,000-tonne cargoes such as iron ore and coal, rose by $1,014 to $21,181. * The panamax index (.BPNI) dropped 108 points, or 3.7%, to 2,849. * Average daily earnings for panamaxes, which ferry 60,000-70,000 tonne coal or grain cargoes, fell by $965 to $25,645. * The supramax index (.BSIS) slipped 73 points to its lowest level since April 2021 at 2,001.