My gf's dad was an airline pilot for 38 years and I've talked to him about this specific topic. You can also find other Reddit posts about the subject.

Yes, they do try and dump fuel over oceans and rural areas, usually at minimum of 6k ft., and they coordinate with Air Traffic Control, but sometimes emergency dumps are necessary, especially if they have to make an emergency landing. Usually the fuel just evaporates into the air.

You wouldnt need to know exact weight, though, just a reasonable estimate, and then slightly overcompensate.

For example, the common B-737-800 maximum take-off weight (MTOW) is like, 175k lbs. depending on the variant. If you have 180 passengers, standard FAA regulations direct pilots to estimate 175 - 180 lbs per passenger, including carry-on bags. So, that's, at most, 32,400 lbs out of 175,000 lbs. FAA also calculates usually 25-40 lbs in stored bags per passenger, with higher estimates in winter months. So, let's say 6,300 lbs of bags. That's under 40, 000 in weight in passengers and bags, out of 175,000 lbs.

Then, the plane can hold around 6,875 gallons of fuel, weighing about 46,000 lbs.

The dry weight of a 737-800 is 91,300 lbs.

So, the plane fully fueled with a full capacity plane with passengers, carry-on and stored bags would be 176,000 lbs.

Not a lot of wiggle room, right? However, the max range of the plane is around 2900-3100 nautical miles, which is about the distance from Miami to Anchorage. The 737-800 is the most popular, workhorse plane configuration in the US, and usually is used for short-to-mid range flights, such as LGA to ORD or MIA.

So, the pilot doesn't need an entire tank of fuel on those flights. However, depending on whether they're flying into the wind or with the wind, and what kind of path they need to take, they can determine how much fuel they actually need to get where they're going, and then add a little extra in case they have to divert or circle the airport.