Would increasing something in size change the speed of its movements ? Example: if a human doubled its size, would it run faster, slower, or the same speed?
Depends on mass, not size. Say a giant weighs 50 kg and a midget also weighs 50 kg. The size wouldn't matter. Other factors would come into play. But practically speaking, a double in size would definitely increase the mass so the answer to your question is indirectly yes. (But it is not a proportional increase.)
I'm just going to give you something to think about---
Let's say two men are going to walk for 3 hours. The inseam measurement for one is 30 inches and the second man has a 34 inch inseam.
If each has a "normal" stride motion, how much ground will each one cover.
(Think isosoles triangles.)
(Also, remember, you can only multiple size so much before the resulting animal's structure can support itself.)