Who cares if he wears weights? There is only so much training you can do to increase your speed before you need more chakra to increase it further, or you just need to be born fast.
Some ninjas are born fast and strong, Minato, Raikage, etc.
Some ninjas use chakra to boost themselves to those speeds, like Sasuke. He wasn't normally that fast but when ninjas want to go faster they pump chakra into their feet to go faster. This is a waste of chakra though so training normally won't drain you as much but it does take longer. When Sasuke copied Lee's speed this is what he had to do, that is why it wore him out more than it would have tired out Lee.
What I am talking about is basically the body flicker technique, but for a longer period of time. It is what the raikage does with his raiton armor. I think at some point it was actually called the raiton body flicker. Any ninja can make themselves go faster just by using chakra, but the more they train for speed the less chakra they will have to use to move that fast. People with large chakras will always have the advantage because they can throw more chakra ito going fast, it is just that often they don't need to.
There comes a point where training won't make you any better, you have to be born with high chakra levels and the ability to go faster. That is why no matter how fast Lee might work to become, someone like Naruto or the raikage will always be able to go faster, just because of access to huge chakra supplies to augment their speed.