Answer

This is a Fermi problem - you're supposed to make reasonable assumptions, and try to estimate all the information you need based on some things you already know. How do we estimate the wieght of anything? Well density tell us the mass per unit of volume, so we can find mass as density times volume. So first we need density of water - assuming you don't already know it. If you've ever lifted a dumbell and picked up a water bottle, you can probably guestimate that one litre bottle of water is around the same as a 1kg dumbell. So $1l = 0.001m^3$ of water weighs around 1kg, meaning the density of water is around $\frac{1kg}{0.001m^3}=1000 kg/m^3$

Now we need the volume of the ocean. Volume of anything is its surface times the depth. Deepest point of the ocean was around 10km, so say average ocean depth is around 4km. If you've ever looked at the world map, you know most of it is water - so let's say around $3/4$ of Earth's surface is ocean. Surface of a ball of radius $r$ is $4r^2\pi$. So volume of the ocean is around $\frac{3}{4}\cdot 4r^2 \pi \cdot 10km$. You might or might not know that Earth's radius is around 6km - I didn't when I was asked this. But I know circumference of a circle with radius $r$ is $2r\pi$ - so let's estimate the Earth's circumference.

My flight from Paris to New York took around 8h, and planes go at around 800km/h. So the distance is around 6400km. New York is 6h behind Paris, so I'm crossing around 6 timezones in between. There are 24 time zones in total so my trip from Paris to New York probably spans around $\frac{1}{4}$ of Earth's circumference. Although New York - Paris is not at Equator level so let's say its $\frac{1}{5}$. Then Earth's circumference must be around $5 \cdot 6400km = 32000km$. From our formula before, that must mean the Earth's radius is around $\frac{32000km}{2 \cdot 3.14}\approx 5000km$. Close enough. Plug this into the volume formula we derived before: $V=\frac{3}{4}\cdot 4(5000km)^2 \pi \cdot 10km \approx 2.2 \cdot 10^9 km^3$. Our water density was in meters so we turn this to $2.2 \cdot 10^18 m^3$. Putting this together, the mass is volume times density: $m = 2.2 \cdot 10^18 m^3 \cdot 1000 kg/m^3 = 2.2 \cdot 10^21 kg$. Nobody really knows the answer but concensus is around $1.4\cdot 10^21 kg$ - close enough!