What factors influence movement speed?

In the original Dark Souls, movement speed was only affected by equip load. In DSII, they introduced a stat called 'Agility' that influences movement speed but also still have equipment load.

How is movement speed calculated in Dark Souls 2?

Similar to the equipment load breakpoints in previous Souls games, if your equipment load is over 70%, you'll roll with a special "fat roll" animation, which is significantly slower and shorter in range than normal rolls. In contrast, any amount of load below 70% seems to use the "standard" roll animation.

In general, the lower your equipment load is (in terms of percentage), the faster you'll move and roll. The burden effect seems to be based on a continuous scale -- rather than discrete breakpoints like the previous games -- so if you lower your equipment load by 1%, you'll move and roll only a tiny bit faster. Similarly, the higher your Agility is, the faster you'll move and roll, on what seems to be a continuous scale.