The first thing to realize is that the moon is in its ‘new’ phase, so whatever gravitational effects you might expect during a total solar eclipse also happen any time there is a New Moon, which happens every 28 days.
Starting as an observer on the ground, you are under the gravitational influence of Earth, the moon and the sun. At the time of the August 21, 2017 eclipse, Earth will be 151.4 million kilometers from the sun, and the moon will be located 365,649 km from the surface of Earth. Using Newton’s Law of Gravity, we can calculate the force of the sun, moon and Earth on an 80 kg person. Earth accounts for 784.1 Newtons of force (176.42 pounds), the moon provides 0.0029 Newtons (0.01 ounces) and the sun provides 0.4633 Newtons (1.6 ounces). But because our Earth rotates, this also provides an ‘anti-gravity’ centrifugal force we can also calculate. So if we add the forces with their correct directions we get a total gravitational force of 784.1 – 0.0029 – 0.4633 = 783.634 Newtons or 176.317 pounds. So, you will be about 1.7 ounces lighter!