I think the real problem of the Valar doesn't have anything to do with being lazy nor not caring about Middle-earth. I think their problem comes from the lack of understanding and comprehension of Melkor's way of thinking and what he's going to do. My point is that they did not do such a good job dealing with the themes of Melkor. Iluvatar allowed things to stand as they were because He could create greater glory through them. Yes, they created the world, but that was not the problem. The problem was a lack of understanding of their enemy and of their charges. I understand that their limited understanding of the inhabitants of Ea is because they were the Theme of Iluvatar alone. However, their lack of understanding of Melkor is a tremendous problem on their part. In order to successfully defeat an enemy you need to understand them, how they think, what they are going to do, and how you can effectively counter their moves. Yes, they ultimately defeated Morgoth but only after much ruin, loss, and suffering. And evil still continues. The best wars (aside from those that don't happen at all) are those that are as brief as possible. The war between Morgoth and the Valar went on for centuries, the Valar seemed unable (or unwilling) to strike a decisive blow. When they did eventually defeat him the Valar had him penned up, but then turned him loose. Big mistake. None of this is intended to say that anyone in their position would have done any better. Depending on your view of fate in Middle-earth, one could be led to believe that this was all determined beforehand to show that Iluvatar is the only One who gets it right all the time.
I'd add to that the Valar feared to attempt to wrest control of Middle-earth again by force as they did when they overthrew Utumno in the Ages of the Trees to the aid of the Elves. In that war Middle-earth was broken and ruined in many places and the Valar feared to do that to mankind who were acknowledged to be 'more frail, more easily slain by weapon or mischance.'
Now, for the Third Age...
Eru, helped in a singular, very important way. It was Eru who sent Gandalf back from his death and gave him greater powers and enlarged his role. Eru does not interfere in the events of Arda often either: only in this instance and in the destruction of Ar-Pharazon's fleet and Numenor.
The Valar's method of helping in the War against Sauron was by sending the Istari. Apparently realizing that in previous instances they had aided the Children of Iluvatar too greatly and directly, and at great cost to the land of Middle-earth, they decided upon a more subtle strategy. Thus, the Istari, or wizards, came in the shape of old men (and were only Maiar) who could not use their full power and were to help the battle from behind the scenes, more or less, rather than fighting Sauron one-on-one. Let's also not forget the Eagles, who were the emissaries of the Lords of the West, and also a sign of "renewed hope and strength." The Ainur also have some subtle involvements by sending prophetic dreams to some of the characters that would help them later in the story.
I'm sure Tulkas, Eonwe, Manwe, and Ulmo would've been able to take Sauron. They could have kicked Sauron's arse and shoved his Ring up it in about 5 seconds flat, but why would they?
Morgoth was a fight that belonged to the Valar. Sauron was a different matter. Sure, the Valar could've sent their forces to dispose of Sauron quickly, but why?
Middle-earth had to prove itself. The Istari were sent to guide Middle-earth; to impart wisdom - not to face-off with Sauron and do all of the fighting for them. Middle-earth would've gained nothing, and another evil would've arisen for them to contend with. Middle-earth cries to Aman. The Valar save the day again. Another evil comes. Middle-earth cries again...get the point? If the Valar had to save the people of Middle-earth, they'd never learn the importance of sticking together and keeping hope. There'd be no point in Middle-earth existing if the people there never learned how to defeat evil. Eru and the Valar seemed to let the people in the Hither Lands fend for themselves, but they were merely allowing them to fight and live and choose for themselves, making mistakes and mending them and making them again. A mother doesn't go on dressing her child after he's grown; eventually he must tie his own shoes, even if he ties them in knots.
