Compared to the usual acceleration of gravity that is almost 9.8m/s^2, it's only a 0.0048 = 0.48%. That is the slope of the real see compared to an ideal sea where there is no gravity from the ice. I'm using a spherical ice instead of a sheet of ice. With a sheet of ice the effect would be much smaller, but I'm too lazy to look up.
The gravity from the ice decrease as 1/r^2 when you go farther. We must integrate the slope to get the volume. I'm going to use a flat Earth, to simplify the calculation, but as the 1/r^2 reductions is quite fast, it's not a problem. With a curved Earth it will be more, but not too much.
Also, we must multiply by 2*pi*r to get the volume in the flat surface all around the sphere instead of the surface of a vertical cut of the sea.
The radios of the Earth is 6371km, so the "distance" to the north pole is 6371kmpi=20000km and we can cut the integral there https://www.wolframalpha.com/input?i=Integral+from+185+to+20... The result is 48,000 km^3 of water. But melting the Antarctic Ice sheet will release 24,300,000 km^3 So it's only a .2% more.
In other units, melting all the Antarctic Ice would increase the sea level like 58m (190ft). The additional effect of the gravity is less than .3m (1ft) And I expect that a calculation if a sheet shaped ice will give a much smaller result.
First, let's calculate the additional high. It's better to imagine the 0 is in the oposite pole, and the additional height is very similar to the old integral without the 2*pi*r https://www.wolframalpha.com/input?i=Integral+from+x+to+2000... i.e.
0.0048 * 185^2 * (1/r - 1/20000)
Now we must integrate it again, with the 2*pi*r Integral from 185 to 20000 of (0.0048 * 185^2 * (1/r-1/20000)), that is only 606km^3, so 1/80 of my previous calculation. So, fixing the last part of my comment with the new numbers:
But melting the Antarctic Ice sheet will release 24,300,000 km^3 So it's only a .0025% more. In other units, melting all the Antarctic Ice would increase the sea level like 58m (190ft). The additional effect of the gravity is less than .0004m (4mm, 1/8 inch)
