Guessing, I expect you'd want two rows of apartments back to back with access space between them, making for something on the order of 50 feet wide, making for 10000sqf area per floor or in very round numbers about 1000 m^2.

The height makes for about 25 floors, so total floor area would be about 25.000 m^2.

Using the weight/floor area values for the WTC (easiest building to find actual numbers for) that would put the weight at 31,250 tonnes.

Looking at the placement of the pivot for your building, and ignoring the bit symmetrical to the short end means you have 120/200 of the building or 18,750 tonnes placed with a center of gravity 100ft from the pivot point.

A counterweight placed 140 ft from the pivot point has to weigh 18,750*100/140 or about 13,400 tonnes.

Made of lead, (density 11.35 t/m^3) it needs to be about 1180 m^3 or, if a cube, about 10.5 m or 35 feet per side.