What is the difference of gravity between lowest tides and highest tides? I know tides are due to gravitional gradients so the difference of gravity between places does not need to be big in order to generate tides.
Regardless, what difference are we talking about, numerically?
This is depending on the location, OF COURSE, so no need to get obsessed about how you could never answer such a question given so little details, etc. Just pick an interesting example or a textbook one, as I want a ballpark figure. Thank you for keeping things simple as possible.
I looked for possible possible duplicates but did not find a question about the numbers.
 A: According to Wikipedia - Tidal force - Formulation highest tide is at lowest total acceleration ($g_\text{total,high}= g-a_\text{tide,max}$),
and lowest tide is at highest total acceleration ($g_\text{total,low}= g+\frac{1}{2}a_\text{tide,max}$).

(image from Wikipedia - Tidal force - Explanation)
According to Wikipedia (Tidal force - Sun, Earth, and Moon)
the tidal acceleration at the surface of the earth caused by another body is
$$a_\text{tide,max} = Gm\frac{2r}{d^3}$$
where

*

*$m$ is the mass of the other body,

*$d$ is the distance between the earth and the other body,

*$G=6.67\cdot 10^{-11}\text{m}^3\text{/kg s}^2$ is Newton's gravitational constant,

*$r=6.37\cdot 10^6\text{ m}$ is the radius of the earth.

So, for the tidal acceleration caused by the moon
(mass $m=7.34\cdot 10^{22}\text{ kg}$, distance $d=3.84\cdot 10^8\text{ m}$)
we get
$$a_\text{tide,max}=1.10\cdot 10^{-6}\text{ m/s}^2,$$
which is about ten million times smaller than the gravity
acceleration ($g=9.81\text{ m/s}^2$) by the earth itself.
Likewise, for the tidal acceleration caused by the sun
(mass $m=1.99\cdot 10^{30}\text{ kg}$, distance $d=1.50\cdot 10^{11}\text{ m}$)
which is much heavier and much further away than the moon,
we get
$$a_\text{tide}=5.05\cdot 10^{-7}\text{m/s}^2$$
which is about half of the tidal acceleration by the moon.
A: The potential energy difference at the surface of the water is $mgh$, where $m$ is the mass of water that you consider, $g$ is the gravitational acceleration at the Earth's surface of about 9.81 m/s$^2$ and $h$ is the difference in height between the tides. It is more convenient to consider the potential difference which is $gh$. For a difference of 1 m between the tides this is 9.81 J/kg.
