You're playing a fine balance between keeping the animal under, and killing it. You have to continually observe and balance the degree of anaesthesia which you can test with pain reflexes and core reflexes, and adjust the dosage accordingly. Too much and you depress the core functions to the point breathing stops. Too little and the animal retains consciousness along with pain reflexes. With larger animals you can use similar equipment to what you would use with humans. Small ones require direct physical observation.
There's a simple dosage rule: n ml anaesthetic per gram bodyweight. So you would weigh the mouse, calculate the dose and then inject it. Sounds easy enough.
Not so. It also depends upon the percentage of fat tissue. If the mouse is fat, the fat tissue will absorb the anaesthetic and then slowly release it. This changes the dynamics of how fast the anaesthetic takes effect, and how deep and how long lasting the anaesthesia will be. Skinny mice would go under almost immediately. Fat mice might take 10 minutes. But if you topped up the dose, you would risk the dosage reaching fatal levels a few minutes down the line as the fat tissue released its stored anaesthetic. You would learn to adapt the formula by experience, but this is just one factor to consider.
Now imagine how difficult this is with obese human patients. Or anorexic patients. Or sick patients. Patients on various drugs. Or patients with different metabolic rates. There are dozens of factors, making each case unique. Anaesthesiologists have a huge responsibility, and taking great care and skill to keep their patients alive. We think of this as routine, and it is, but that doesn't make it simple or easy to do. This stuff looks simple on paper. Doing it in practice is far, far more difficult and demanding.