I think what you're noticing is that parts of the animation are being given more frames, but the total animation isn't actually getting any longer.
If you think of the initial 9-frame animation as 9 equal movement "steps", then when you make the second step a key-frame, and move it into frame three, you now have two steps that lasts three frames, while the remaining six steps only last for five frames. The result is that you're essentially "squashing" a large part of the motion into a smaller number of frames, which has the effect of increasing the effective speed.
Another way of looking at it is that tweening is actually another name for interpolation, which is breaking a single movement into a series of smaller steps. So if you move an object 80 pixels over 9 frames, then each frame is 10 pixels of movement (first frame is the starting point). When you make the second frame a key-frame, it becomes fixed, so now, no matter where you move it, the object will only have moved 10 pixels in that frame. So when you shift it to the right, you cause that 10px movement to take up more frames, and therefore become slower. The remainder of your animation represents the movement from 10 pixels to 80 pixels, but if it now has less frames, then the steps required to do this become bigger.
So, in the first part of Katsu0_0's animation above, if you have the object moving 10px per frame, then when the second frame is made a key-frame and moved to the right, you now have a 10px movement over 3-frames, so the movement occurs at 5px per-frame, rather than 10px per frame like before. However, the other 70px of the movement now only lasts 6-frames instead of 7, so the movement occurs at around 12 pixels per frame, which is much faster.
Dunno if that clarifies it any? I can't think of any good real-world examples where it makes real sense. Except maybe a 500m race; if you do it evenly over the course of 100 seconds then you travel at a steady pace of 5 metres per second. However, if you spend more time on the first 100m than you do on the rest, then you will be slower for the first 100m, which means you have to travel faster to complete the other 400m if you still want to finished within 100 seconds.
Anyway, this is a really good tip Katsu0_0! I've been doing all kinds of stupid things when trying to smooth out animations