Weighing 2 vertical halves of the human body
The two halves likely do weigh approximately the same. Since the density of most tissues that are not filled with air is basically equal, it doesn't matter that, e.g., heart, spleen, and stomach are on the left and liver is (mostly) on the right. In the left/right axis, it evens out.

As for the location of the center of mass of a human: it's located about 10 cm below the navel, at the level of the S2 vertebra approximately midway between dorsal and ventral surfaces of the body (assuming that the person in question is neither pregnant nor obese).