1. Even though the companion star cannot be seen, the elliptical motion of the primary star (once parallax and aberration effects have been subtracted) tells us that there is an unseen companion perturbing the motion of the star that we can see. If we can make detailed observations over a period of time, we may be able to infer masses and orbits for the two stars in the system in the most favorable cases.
2. Stars late in their lives tend to lose large amounts of mass because of very strong stellar winds blowing from their surface. According to our understanding of stellar evolution, Sirius B became a red giant after leaving the main sequence and lost much of its mass in a strong stellar wind that probably produced a planetary nebula. The remaining core of the star, containing only a fraction of the original stellar mass, then became the white dwarf Sirius B. Since Sirius B has evolved faster than Sirius A, this implies that the original main sequence mass of Sirius B was probably considerably larger than the present mass of Sirius A.