Is the weight of water that you’ve already drunk that much different from the weight of carried water?

My general practice is to drink around 0.5 to 1 liter of water if I arrive at a water source and I am thirsty. I simply drink until I feel totally quenched. Then I fill my bottles up with however much water I think I'll need for the next stretch of the hike (before the next water source).

I find that this 0.5 to 1 liter water consumption is just about right for me. It gets me to a point where I'm not thirsty anymore, but it's not so overkill that I feel sick to my stomach afterwards and immediately pee it out.

Everyone is going to have their own preferences, of course, but it sounds like my own practice isn't so far out of line with many other out there.

Rather than relying on intake, I tend to look at output (admittedly easier for pointers than setters).

My MD wife focuses on 30 ml/hour as the minimum output for proper kidney function. You can pass a LOT more water than that, but passing LESS than that indicates you are under-hydrated. So one approach is:

"Could a shot-glass per hour with my pee?" and/or "Did I pee in the last few hours?" If not, drink MORE.

The colorimetry approach is, "Was my urine noticeably yellow/dark?" Then I need to drink more.

The Blood Bank assesses hydration by the tenting of your skin when they pinch the skin on the back of your hand. When I try to change that, it can take 12 to 24 hours of consciously greater input to turn it around.

I monitor urine volume and color for feedback on short-term hydration issues.

I assess skin tenting and my weight (I can estimate my weight to within a pound) for managing longer-term (24-48 hours) hydration issues.

Back to the OP: If you are passing a lot more than 30ml/hour, yes, you could have hydrated less and carried less weight for the previous miles.

the OP's question is precisely why I half seriously suggested in another thread that weight carried should include both the weight of all gear and body weight.
problem solved …

If nothing else, a "camel" approach saves weight in water containers. I don't think anyone is suggesting drinking 3 liters, but by being willing to chug back a liter if needed one can make do with a bit less capacity.

Capacity entails weight, but not much. Maybe an 1-1.5oz saved if you chug a liter instead of packing it. A more salient difference is bulk. If you're packing 5-8 liters in the desert that's a lot of space. I'm heading on the PCT this summer and I want to bring my medium pack (ULA Ohm) rather than my 1 lbs heavier big pack. Drinking water when its available is a small part of keeping my load size manageable.

I think we all agree there's no reason not to drink up within reason, but trying to chug 3 liters is stupid. More important than any of this is carefully planning your water. That means not carrying 4L when you need 6, and it also means not carrying 6 when you need 4. Carefully managing the latter is where appreciable weight savings lie.