I know we see effects, supposedly.We definitely see some effects: the orbits of the stars and their timings.
What *seems* grandiose is that they base all their conclusions on effects only.Not grandiose conclusions at all: determining the mass is old hat and the size is limited by the fact that the orbiting stars do not collide with whatever is there. The only conclusion that fits that observed facts is that there is a black hole.
Of you observe poop, does that mean you now understand the animal it came from?
Ok, that makes sense.The timing of the orbits allows the determination of the mass. A faster orbit at a given distance is associated with a higher mass. This is pretty standard and well tested. it's how we knew the mass of Jupiter before actually going there (watching the orbits of its moons).
It's mass has been (or can be) measured? How?Once again, the orbits of the stars close by is what gives us the information we need to say it is a black hole, from its mass to the size of the region is occupies. Like I pointed out, we are even measuring the warping of space in the region by measuring the precession of the orbits of those stars. Sixteen years of data there gives a lot of relevant information.