Yes, it is a choice. Or more specifically, you must pull the creature, but you can pull him 0 feet.

Thorn Whip
You create a long, vine-like whip covered in thorns that lashes out at your command toward a creature in range.
Make a melee spell attack against the target. If the attack hits, the creature takes 1d6 piercing damage, and if the creature is Large or smaller, you pull the creature up to 10 feet closer to you.

The spell does exactly what it says. Many spells and abilities give you the ability to choose, by including the appropriate wording. This one specifically allows you to choose the length you pull the creature (0-10 feet).

The important part of that attack option is this:

And the water weird can't constrict another target

This same terminology is used of creatures like the Tarrasque who have the 'Bite and Swallow' feature or a Kuo-Toa Whip's Pincer Staff.

This means that the Weird cannot Constrict any target other than the one that it is presently constricting. So it can repeat this attack against the same target every round, in addition to the fact that you are being held underwater. Most likely, it will kill you by crushing rather than killing you by drowning.

In fact, the lore comments on it even makes it clear that it is trying to crush you.

[...] using its coils to crush any creature other than its summoner [...]

One other point of note when fighting a Water Weird: It has a 10' reach, and can fight just fine in deep water. The party may have a difficult time reaching it if it is sitting in water too deep to stand in. This can make it a little extra challenging as well if the party has to jump in and try to swim in order to fight it in melee.