Why do we measure starters in terms of liquid volume instead of weight of the sugars?

It seems like it makes more sense to measure the starters in terms of how much sugar you are putting in for the yeast to eat... Wouldn't a 1L starter with 8oz of DME work better than a 2L starter with 6oz?

Well most starters are made at a specified OG, so the amount of sugar added is inherent in the initial volume of the starter. I'm sure the most effective OG for a starter was a subject of some studies, and 1.030 to 1.040 was found to be the best. Adding more sugar just stresses the yeast more.

As priceless said, you don't want to give the yeast too high of an OG in the starter. You want them to focus on multiplying and creating strong offspring. If you get them too excited (high OG) you wind up with lower quality yeast. If you need more yeast than you can get with a moderate gravity starter (1.040), then you really need to perform multiple steps to increase the quantity, not attempt to use brute force and force feed them.

I agree with everything above. 1.030 to 1.040 is recommended. Mine end up around 1.045 because that's the only way I can get the cell count I want in two steps without getting a 3L flask.

As above, when someone says a 1.5 litre starter, they mean a 150g DME topped up to 1.5 litre with water. Everyone is following the standard recipe of 100g DME per litre of starter.