There were effectively 3 reasons why a state might want to ratify the 13th Ammendment. Roughly in order of how quickly it would motivate them to take action:
- Its residents agreed with it and wanted it to become law.
- The state was a former member of the Confederacy, and wanted its own full voting rights restored.
- It had passed anyway, but the state wanted to not look racist.
If your state simply thought it was the Right Thing To Dotm, then it would have passed it regardless of any other political considerations, and probably quite quickly. As for the rest...
In the wake of the Civil War, there was a huge political fracas on what the process would be for the former rebel states to demonstrate their fitness to rejoin the Union with full voting rights. Andrew Johnson, a southern Democrat who'd been selected VP as a unity gesture, ended up POTUS after Lincoln's assassination. He took a very "moderate" view that national ratification of the 13th Amendment was all that was required. As administration of the defeated states was largely a military matter, as Commander in Chief he had all the authority he required to make this a fact. This is the situation that induced Tennessee, Arkansas, South Carolina, Alabama, North Carolina, and Georgia to push the 13th over the edge to taking effect in 1865. Once that had happened, no further ratifications were required to put it into effect, so no further Confederate states did so for years (aside from Florida, who probably had theirs in process at the time). However, this wasn't enough for Congress, who refused to readmit these states until more tangible measures were taken.
Texas was also possibly motivated by readmission, in that they were not readmitted to the Union until 1870, about a month after they ratified the 13th.
Note also that this is a simplification. States under military occupation aren't exactly known for producing free and fair elections, and there were definitely shenanigans going on with these ratifications. OTOH, most of these states were allowing black men to vote for the first time, which arguably made their elections much freer by modern standards than they had been previously, even with the Federal troops.
This leaves the states of Delaware, Kentucky, and Mississippi. This first two were slave states that remained loyal (and thus didn't need readmission). Mississippi had resisted to the point where it became clear passing the 13th wouldn't help them rejoin. They were readmitted to the Union in 1870 along with the other remaining three states, Virginia, Texas, and Georgia.
This means the only remaining motivation for a state to ratifying after 1870 would be a desire to not look racist. Mississippi was always the state with the highest proportion of black residents (D.C. aside, they still are), and throughout the Jim Crow era enforced white supremacy via both legal measures and terrorism. During this era they certainly weren't going to be interested in taking measures to reaffirm the rights of black residents. Looking racist was in fact the point.
So it wasn't really until the modern era when Mississippi had sufficient motivation to ratify it.