Chakra is internal energy; it has nothing to do with physique (muscle, bones, skin, organs, etc.). Ninjas do not train their physical mortal bodies, besides special cases like Lee and Gai. The reason why Kakashi and Obito could move is because they have superior physique compare to Sasuke and Naruto, who have never trained their bodies before. Because gravity increases the weight of everything, chakra cannot help here. The only thing that can help is pure physical strength, and Kakashi had trained with Gai many times and was even able to open the first gate, meaning he is stronger physically.
This is also called the "Container" and the "Water". A ninja's essence is chakra, which is an energy located within the stomach and runs through the chakra network. So, in this case it is the water. The container is the body/physique of the ninja. A ninja does not need a strong body to become powerful, since chakra can be used to increase speed, jumping, power, etc., but remember that chakra does not change the structure of a ninja's body, such as bones, muscle, organs, etc. This is why Gai and Lee train their bodies so that when they open the gates it does not rip them apart. Sakura, for example, uses chakra control.
Kishimoto knows this, but the viewers don't, and he indirectly already confirmed body and chakra are different when he introduced Lee and Gai. Most viewers see chakra as more physical strength and more speed, but they don't realize that chakra and physique/body are completely different categories.
Example. Suppose that one denotes the following:
Level 1: Human Adult Male
Level 2: Bodybuilder Male/Power lifter
Then, an average ninja's body is of level 1, exactly as it was since the day they became able to extract chakra. Most future ninjas learn chakra extraction by the age of 4–7, which is the time they enter ninja school. Before learning chakra extraction, they are just normal humans: no super-strength or anything.
Naruto/Sasuke's body is of level 2, slightly higher even though they have never done training for physique, just because they are talented individuals and have bloodlines/tailed beast since birth.
Continuing the analogy in a similar manner, Kakashi is of level 4, since he trained to open the first gate.
Lee is of level 20, since he trained enough to make muscles, bones and body stronger to survive gates being release up to the sixth gate.
Gai is of level 30, since he can survive without breaking bones up to the seventh gate.
All ninjas can use chakra to directly enhance power/speed depending on their chakra levels and chakra control. Some, like Tsunade and Sakura, have extremely talented control, and are thus able to create similar feats of superhuman strength when they fight. Others like Kakashi are lower tier when they fight in close combat, as seen with his fight against Obito, while Lee and Gai do have stronger bodies, but because they have bad chakra control their increase in physical attributes from chakra enhancement is not similar to Tsunade and Sakura.