Sun dipped Superman moved approximately 4.3 Octillion tons/4,325,781,841,303,900,090,000,000,000 tons
This happened post crisis and I don't know if anyone ever did the calculations. When Superman moved war world which has thrusters that enable it to move beyond light speed, he moved approximately 4.3 Octillion tons.
Superman said war world had the same mass, size etc... as Pluto.
Pluto's mass is 13,090,000,000,000,000,000,000 kg which is 14 Quintillion tons(14,429,255,060,000,237,568 tons specifically)
Since war world's thrusters enable it to move beyond light speed and it used it's thrusters in an attempt to prevent Superman from pushing it, you'd have to apply the momentum = velocity(m/s meters per second) x mass(kg) formula to get the true mass that Superman was actually pushing which would be far beyond just Pluto's mass.
13,140,000,000,000,000,000,000(Pluto's mass) kg x 299,792,458(speed of light in m/s) = 3,924,283,275,000,000,000,000,000,000,000 kg
In tons that would be 4.3 Octillion tons(4,325,781,841,303,900,090,000,000,000 tons)
To get more of an idea of how astronomical this number is, the combined mass of every planet in our solar system in tons is approximately 2.9 Septillion tons(2,940,408,474,000,000,000,000,000 tons).
You would have to multiply that combined mass by 1471 to get 4.3 Octillion tons. So basically, Sun dipped Superman practically moved the weight of 1471 solar systems that consist of planets with an equal amount of mass as our solar system's planets.
You would also have to multiply Earth's mass(6,583,212,587,989,520,610,000 tons) by 657092 to get that mass. Sun dipped Superman practically moved the weight of 657092(well over half a million) planets all at once that each have an equal mass to Earth.