yes, I belief it is based on weight only. As you start carrying more and more, the weight indicator starts changing color, but when researching this I found out that that is just an indication and doesn't directly affect speed.
As for NPC's, this might be different however. When creating an NPC with the quest script, you can set a speed value, so it is not soley dependent on weight for them. further research is needed there.
Also you can increase speed somewhat with drugs, though I cant remember which one.