That high-speed winds are accompanied by a reduced air pressure.
Blowing between the balloons creates a region of fast-moving air, and therefore a region of low pressure, in the gap. The air surrounding the balloons on their outer sides is still at ordinary atmospheric pressure, which is now higher. That higher pressure pushes each balloon inwards, towards the low-pressure region — so they meet in the middle.
Air blown fast through the gap → pressure in the gap falls
Pressure outside the balloons = atmospheric (higher)
Net push on each balloon is inwards → balloons move together
Blow harder → bigger pressure difference → they move faster
Where this leads: the same rule explains roofs being blown off in a storm, holes cut in banners and hoardings, and why loose sheets and papers are pulled towards a fast-moving vehicle rather than pushed away from it.