Well, let us look at all the things computers do not like.
Heat
Violent Shocks
EMP
Voltage spikes
Cosmic Rays and the list goes on.
Now let's look at what it will take to put a computer on a combat spacecraft to protect it from damage plus all of the above.
One ton sounds about right.
I was once at a demo where a guy put an iPad in an armored case and chucked it at a wall, and the thing kept working. I'm pretty sure it didn't weigh a ton. More to the point, avionics in modern fighter aircraft are very lightweight. EMP shielding is sophisticated, but not particularly heavy.
When you really think about it, compared to the computing power necessary for flight assist, let alone hyperspace jumps, the docking algorithm is trivial. Automated docking should just be an app for your already existing on-board computer.
I get that they are going for the nostalgia of the docking computer from the original Elite game, but in reality, it is a bit much given that we are talking about technology from a space-faring society over a thousand years in the future.