The weary of the Negro Question and the sick of carpet bag government signifies the Northerners tiredness in trying to solve the race problem in the South and also were suspicious of what they were beginning to see as a corrupt government. I hope you are satisfied with my answer and feel free to ask for more
"weary of the 'Negro Question'" and "'sick of carpet-bag' government." are related to the same political, social end economical event that happened in the USA after the end of the Civil War: The Reconstruction era. Congressional Reconstruction included the stipulation that to reenter the Union, former Confederate states had to ratify the Fourteenth and Fifteenth Amendments. Congress also passed the Military Reconstruction Act, which attempted to protect the voting rights and civil rights of African Americans. Former Confederates resented the new state constitutions because of their provisions allowing for black voting and civil rights, where we can explain the "weary of the 'Negro Question'". Carpetbaggers were northerners who allegedly rushed South with all their belongings in carpetbags to grab the political spoils were more often than not Union veterans who had arrived as early as 1865 or 1866, drawn South by the hope of economic opportunity and other attractions that many of them had seen in their Union service. Many other so-called carpetbaggers were teachers, social workers, or preachers animated by a sincere missionary impulse.
