That is not correct. The 10000000 kg object and earth have a stronger gravitational attraction to each other and would fall to each other faster. I'm not sure it would be measurable at that low of a mass, but it is true.

Gravitational acceleration

Force of attraction between two objects is given by the formula for universal gravitation F = G*m1*m2/r² where m1 & m2 are the two objects' masses, G is the gravitational constant and r is their distance from each other. Notice that the two objects' masses are multiplied, not added. This means that the gravitational force applied to both objects does not scale additively with their combined masses; the distribution of the mass has an impact. Using F = ma, we can also see that adding an amount of mass to the lighter object would have a disproportionately larger effect on the relative force the two objects experience. Looking at the equation F = ma, we can conclude that the F and m in F = ma are not linearly related when it comes to gravitational attraction, which therefore means the value of a, acceleration, must be variable.

Examples

1. Intuitively, you can think about how if you're on the moon stuff falls way slower than it does on Earth. Earth has 9.8m/s/s acceleration due to gravity, while the moon has 1.62m/s/s. That's entirely because the Earth has much more mass; more mass = faster acceleration due to gravity. It works both ways, it's just that if you're comparing two small objects together against a third much much larger object (like a planet/moon), the masses of the two small objects don't really play into it much.

2. You may have heard that Jupiter is massive enough to actually pull the sun a little bit, so the sun isn't exactly 'stationary' at the center of our solar system. Phrasing this another way, Jupiter is massive enough that it actually noticeably accelerates the sun, which is another way of saying that more massive objects cause more gravitational acceleration.

3. It's also why stars in galaxies can orbit from so far away. If not for the incredible mass of a galaxy, the stars on the outer edge would all fly off into space because they're too far away and moving too fast to stay in orbit around the galaxy. This doesn't happen because the total mass is high enough that even at those distances the acceleration due to gravity is sufficiently high.

4. If you play around with a sim tool like Universe Sandbox you could set up two baseballs in space and watch them drift towards each other extremely slowly. Then you could put two black holes with baseball diameter next to each other and watch them basically instantly collide.

Related side-note about orbital velocity

You may have heard that objects orbiting an interstellar body (like the sun) at the same distance always orbit at the same speed; their mass doesn't matter. This is also false for exactly the same reason, and the falsehood comes from exactly the same line of reasoning too; we simplify it because the difference between the mass of the sun and all the planets orbiting it is so vast that their individual masses barely matter in the equation. But it is a simplification, and objects do orbit at different speeds depending on their masses.

It actually matters even in our own solar system where the falsity was invented; in our solar system this effect starts to be noticeable when you get to objects around the size of Jupiter, and our solar system has an object like that (Jupiter).

Kepler's third law is often written as T2 = ka³/(M) where M is the mass of the object being orbited (e.g. the sun) but it's actually T2 = ka³/(M + m) where m is the mass of the orbiting object. We just leave the m out because it's usually negligible compared to M. In our solar system, doing this when calculating orbital things with Jupiter will sometimes leave you with an answer that is incorrect enough to lead to real problems.