Effects of pressure at sea level
The effect of atmospheric pressure on sea level is described as "inverted barometer" effect. The basic equation governing the effect (Wunsch &amp; Stammer, 1997) is: $\delta_{IB}  = -{\Delta P_{atm} \over  \rho_{water}*g}$, where $\delta_{IB}$ is the change in sea level, $\Delta P_{atm}$ is the change in atmospheric pressure, and $\rho_{water}$ is the density of water.

A good example of the effect was observed by Close (1918)
 From Wunsch &amp; Stammer, 1997.

In reality, while atmospheric pressure can vary between 870 and 1070 mb, the problem is that it might result in a change of 2m over a distance between high and low pressures that could be many hundreds of km. By comparison, the sea level gradient across the Gulf Stream is on the order of 1m/100km. The other problem is that the ocean adjusts dynamically to the differences in air pressure and the resulting sea level gradient might be smaller.

To convert pressure to force (acceleration), you can use $P=\rho g h$. The biggest differences in $g$ at the surface of Earth are around 50 mgal (50 $\mu m/s^2$) and caused by differences in latitude, altitude, and local topography and geology. The differences in gravity cause by the extra meter of water will be way smaller and can be considered negligible.



Wunsch, C., and D. Stammer (1997), Atmospheric loading and the oceanic “inverted barometer” effect, Rev. Geophys., 35(1), 79–107, doi:10.1029/96RG03037.

Close, C. (1918), The Fluctuations of Mean Sea-Level with Special Reference to Those Caused by Variations in Barometric Pressure. The Geographical Journal 52, no. 1, 51-58.