Jan 21 (Reuters) - The Baltic Exchange"s dry bulk sea freight index (.BADI) fell for the eleventh straight session on Friday, en route to its second consecutive weekly decline, tracking weaker rates across all vessel segments. * The overall index, which factors in rates for capesize, panamax and supramax vessels, fell 59 points, or 4%, to 1,415, its lowest since mid-February 2021. * The index has lost nearly 19.8% this week. * The capesize index (.BACI) dropped 140 points, or 13.6%, to 891, its lowest since June 2020. The index is down 40.4% this week, its biggest drop since the week ended Dec. 17. * Average daily earnings for capesizes, which transport 150,000-tonne cargoes such as iron ore and coal, dropped by $1,157 to $7,390. * Meanwhile, Chinese iron ore futures rose around 3%, posting a third straight weekly gain amid hopes for strong demand, fuelled by Beijing"s fresh stimulus measures, while steel prices were range-bound as production curbs at mills weighed. * The panamax index (.BPNI) slipped 14 points, or 0.7%, to 2,010, its lowest since mid-April 2021. The index was down 15.3% for the week. * Average daily earnings for panamaxes, which ferry 60,000-70,000 tonne coal or grain cargoes, fell by $133 to $18,087. * The supramax index (.BSIS) fell 24 points to its lowest level since end-February 2021 at 1,749.