First, answering your text questions:
Yes, it can constrict the same target again.
Actually, I think this is the point. The block states
and the water weird can't constrict another target.
And nowhere it says it can't constrict the same target again. This is also confirmed by this answer.
It can also just change targets
Until this grapple ends, the target is restrained, the water weird tries to drown it, and the water weird can't constrict another target.
From the Grappling section on PHB:
The condition specifies the things that end it, and you can release the target whenever you like (no action required).
So, the Water Weird can just release the current target, ending the grapple, and then constrict another target.
it stops being a threat as long as it's grappling a character?
This part of your question is off. That is not how Water Weird/Constrict is supposed to work.
About your title question
Your setup is kinda suboptimal for the Water Weird
As I read his stat block, he is supposed to be fighting under water. In particular, this feature
Invisible in Water. The water weird is invisible while fully immersed in water.
is completely lost in your setup. This should decrease the challenge of the party considerably.
So, I would say
Yes, in your setup, it might be too weak for three 3rd level PCs
But not for the reason you thought, but because it loses a major feature - permanent invisibility.
As a Side note on resistances and immunities
You didn't mention your PCs' classes nor their items. So, I would like to add a caveat to my answer.
Damage Resistances: fire; bludgeoning, piercing, and slashing from nonmagical attacks
Damage Immunities: poison
So, if your party is too martial-based (e.g. a Fighter and a Rogue) and these martial PCs don't have magical weapons yet (which is likely by 3rd level), the resistance to physical damage can make the fight harder again, changing my answer.
As a final note
A CR3 monster has 700 XP on it. Against your party, it means a barely Hard (675 XP threshold) encounter. It's far away from a Deadly encounter (1200 XP threshold). So any CR3 monster shouldn't be that hard, even by book's definition - hard encounters mean there is a slim chance that a PC dies.
These XP thresholds can be calculated using Basic Rules or DMG section on Creating Encounters.