Why small bubble rises slowly through a liquid whereas the bigger bubble rises rapidly?

It has to do with bouyancy and drag much like a kilo of loose gravel will fall through the air faster than a kilo of loose feathers. Both of them have the same force of gravity working to pull them to the earth, the feathers just have a larger surface area to drag through the resisting air. The ratio of surface drag to pull is greater for the feathers than for the gravel

small bubbles have a larger surface area in relation to their volume than large bubbles do.

Drag is proportional to the surface area

If you model bubbles as perfect spheres (they aren't, of course, but the general affect is the same)

the surface area of a sphere increases as the square of the radius

A = 4πr²

yet the volume of a sphere increases as the cube of the radius

V = 4πr³/3

so a larger bubble displaces more water per square area.

As the lifting force on the bubble is proportionate to the volume of water displaced, the ratio of lifting force to retarding drag is greater for the larger bubble than for the small. The big bubble rises faster.

Bubbles in liquid are essentially air pockets and air is less dense than water. So therefore the bigger bubble contains more air so will rise alot quicker. It's the same as if u fill two different balloons with different amounts of helium, the one with more helium will rise quicker

Because the KE of the small bubble is low than the KE of big bubble.