It sounds like you have a motorcycle with a carburetor with gravity fed fuel line. (i.e. Without a fuel pump of any sort). In those conditions I can see that there is a higher fuel pressure at the inlet to the carburetor when the fuel tank is full. It's possible that when the tank is low the pressure is barely enough to meet fuel demand.
With that said, you need to improve fuel flow between the tank and the carburetor. Fuel line and petcock could be too small (diameter). You could have a partially clogged fuel filter or residual crud in bottom of tank restricting fuel flow.
It is also possible that your carburetor's fuel bowl system isn't working correctly. The fuel bowl in the carburetor acts as a little reservoir of fuel to ensure there is always fuel available to meet fuel demand.
I'd start with checking the filter and tank for dirt and crud. Let us know what you find!
Update:
Hmm. I watched that video before I responded.
What you are describing sounds like the newest religion. You just gotta have faith.
I will say I'm not a rookie at this stuff. I worked at a Detroit car company where I managed the sale and engineering of millions of fuel tanks. I'm more than familiar with fuel tanks, pumps, carbon canisters & reservoirs. I'm really good in troubleshooting related issues.
What you are describing on your car is fooey. Facts not in evidence. Pure snake oil. "You can see it if only you are a true believer". Ditto for the person in the video. (Or he just has a clogged fuel filter :^). You probably shouldn't believe everything you read on the internet.
And on your bike if you do have a true measurable difference in acceleration do check for dirt and debris between tank and carburetor. Hint. A measurable difference here implies the use of a dynamometer (or simple stopwatch on a measured and marked distance, given exactly same conditions except fuel level in tank. )
