Why did the small people of Lilliput first try to attack Gulliver but then provide him with food?

The Lilliputians, for all their tiny, doll-like prettiness, never do anything for nothing. Therefore, their sheltering and feeding of Gulliver—and feeding him admittedly takes a huge amount of their resources—arises from a calculation that he can do them good.
They primarily see him as a war weapon. Because of his size, it is as if they have a acquired an army. They want him to be on their side and to help them destroy their Blefuscu enemies, who they believe are preparing an attack. They also use him for heavy labor, as he can easily perform tasks that would require a great deal of effort on their part. He can be used as well as a beast of burden to carry messengers to and fro.