This whole passage is quite ironic.
The name Balak means "devastator," a very evil name. However, his father's name, Zippor means "sparrow," which are among the flightiest of birds. A person cannot creep close to a sparrow, as they fly at the slightest movement. So, here is mighty Balak, the Devastator, the son of Zippor, the Sparrow, and "Moab was exceedingly afraid"! The Devastator was afraid, acting like a sparrow!
The Moabites were so afraid that they were "sick with dread." Hebrew is a rather colorful language. This means that they were so terrified that they were throwing up. Their fear was visceral; it made their guts wrench. What makes this so ironic is that they had nothing to fear: God had told Israel not to harm the Moabites but pass them by (Deuteronomy 2:8-9). If Moab had left well enough alone, if they had not let their fear get the best of them, then nothing like the following story would have happened. Many people died because of Moab's fear and the resultant actions. In reacting to their fear, they really made a mess of things.
Another irony is what is said in verse 4 concerning a possible economic problem. Moab says that Israel would come through and "lick up" all of their goods, that is, eat all their wealth. At the time, their wealth was mostly on the hoof or in their grain storehouses. They thought Israel would come in, take all their livestock and grain, and leave Moab destitute. Again they had nothing to fear because God was still giving them manna six days a week and double on Friday. Israel was not going to invade, devastate their land, kill their people, and take all their wealth. Thus, the second element they feared was also bogus. They had made it all up in their own heads; their fears were figments of their imagination.
They were functioning by human nature, and it was only natural for them to think that, if two or three million people came in, they would eat up everything and take over the territory, but that is the irony of all this. Nothing like that would have happened, especially if they did not move to make Israel their enemy.
All of this could have been avoided with a little bit of communication between Balak (the Devastator) and Moses. If he had come to Moses instead of Balaam, everything would have worked out differently. Instead, Balak makes some sort of alliance with the Midianites, who, as the book of Judges details, became a thorn in Israel's side. Thus, here is the beginning of an alliance against Israel that lasted for many years.