What Walt is saying in this article is that states have two possible reactions when some other state becomes a danger. They can form alliances either to A) balance the power of the "new" state or to B) "bandwagon" -- that is, to become friendly with the new danger so that it will not threaten them.
Walt says states will tend to balance against threats when
- They themselves are relatively strong
- When there are allies who might help them
- During a war, especially, when the war is serious
He says that states will bandwagon when
- They themselves are weak
- There are few likely allies to help them against the new power.
- In peacetime or at the start of a war