Perhaps surprising since we happen to live in it, we don't know that much about the Milky Way. In fact, we may know more about some other distant galaxies than our own. That's actually a result of living inside the Milky Way, it's impossible to get a perspective view.
This is why most of what we know about the galaxy is inferred from various behavior and phenomena we see, which means that our understanding is only as good as the methods that led us to it.
That's how the mass of our galaxy can vary wildly from estimate to estimate. Some astronomers now believe that the Milky Way is only half as massive as was previously thought.
They determined this by studying the more distant, outer stars in our galaxy. They found that the dispersion of the radial velocity of those stars was far smaller than expected, meaning that the galaxy itself must weigh far less than previously believed.
The speed at which stars circle the center of the galaxy is directly dependent on the mass of the galaxy itself.
Our galaxy is made up of three main regions, the dense central bulge, the flat disc, which houses the sun, and the outer halo which is mostly made up of dark matter but is also home to some stars. It's these halo stars that astronomers observed.
With this new knowledge in mind, astronomers now believe that the Milky Way weighs about 500 billion to 1 trillion times more than our sun.
That may seem like a gigantic number, but it's much smaller than previous figures. The number does include dark matter, which is thought to make up a large part of the mass of a galaxy.
Don't expect this to be the final word, things change fast and new measurements may provide wildly different numbers in the future.