My weapon of choice is the tank. It's shells out-range the worms, only drawback is you have to be close enough to make him come out of the ground, but you can still avoid being too close that he can attack.
Edit: The normal (non-explosive) rounds actually do 90%ish of its HP as well.
There are two really good ways to kill big worms cheaply, the first is laser turrets, they out-range the big worms and rip them to shreds since the big worm has no laser resistance.
The other good way is poison capsules. They out-range the big worm if you take advantage of area damage. Poison capsules stack, you need to throw 4 to kill a big worm - but those 4 capsules can kill a dozen big worms so it's pretty good.
There are also more expensive ways to kill them, like using lots of capsules (defenders work if and only if you have all the bullet damage upgrades, otherwise distractors and destroyers).
Poison is a very good way, and you can get it fairly early, usually before laser turrets or the tank. The distance that you can throw the Poison Capsules from is the same range the Big Works have. So if your just stand just outside their range and throw some capsules at the very edge of the throwing distance (indicated by the green circle when you have some in your hand), they will still damage the worm.
The damage also stacks so if you throw out a whole ton it will kill the worms even quicker. Tank and lasers obviously work well too, but are a bit later tech than poison.
It should be noted though that Poison does not work on Spawners.