You are right in the way you are thinking, but you don't have the full information: in a 600 kg plane the fuel is 100kg. The mass reduction does not make such a big impact, especially as you rarely top the tanks (you can carry more luggage or a heavier pilot & passenger) and you never empty it (30 minute reserve is usually raised to 1 hour reserve), so you have a 10% variation of the total mass of the plane on regular flights: no significant impact.

On the other side, large planes carry a lot more fuel as a percentage of the total mass, it really matters to them.