I am somewhat obese. I am lifting half of what I used to lift when I was 30 lbs lighter. If I were to get back in shape, would my serve speed increase significantly?
Title should read "serve speed", not "service speed"
For service it depends. Just like for any other shot.
What is service speed?
It is the energy that you are able to transfer to the ball, which in turn is compound of: how fast you can accelerate your hand, and how much transferable energy your body can create from the service motion.
I assume that the part with hand acceleration is self-explanatory.
When it comes to the body.
Without seeing and knowing your service motion - it is impossible to answer.
But it can go both ways.
Let's assume that you employ a platform stance and jump. Less weight might result in better jump -> which in turn might translate into more energy passed to the ball.
Or perhaps your legs are so powerful that it will have zero impact on your jump, hence less weight will result in less energy that you can transfer to the ball.
P.S.
The example with heavyweight boxers is a good one.
Those guys are good at:
1. accelerate the hand
2. transfer the body mass into the hit
these 2 combined created a huge energy, in some cases comparable to being hit by a truck.
but at the same time, if you are not good at transferring the body mass into the hit, then losing or gaining weight obviously has less impact on the final outcome.