I ran the number you have on my calculator and came up slightly different, so I rechecked by long multiplication by hand and confirmed what my calculator said - 3.35195 square inches. Then I re-did the calculations using pi to 10 digits and got 3.345871574 but since we started with 3 decimal places for pipe diameter, the result should be 3 also, so 3.346 square inches. I went thru and checked the rest and they're all close enough to what I get, it doesn't matter. I end up with a little over 30 pounds as well.
Or if he's trying to lift the entire water column as a sealed unit.
As for the check valve - there is a little more to it than just the PSI it has to withstand. With a 1 sq inch area at 15 psi the valve only has to resist 15 pounds of pressure. However, with a 2 sq inch at 15 psi the valve only has to resist 15 pounds of pressure just as in the 1 sq inch one, but the rubber diaphram is 2 sq inches so is subjected to 30 pounds - we have to consider "strength of materials" in situations like this.
You will also find smaller diameter pipes rated for higher pressures than larger pipes. A 1" pipe has a circumfrence of 3.14", a 4" pipe is 12.56". So while the pressure is the same, the 4" pipe has to resist 4x the forces because of it's larger surface area.