Why do race car drivers weave from side to side when following the pace car?

They are conditioning the tires or "warming them" to keep them sticky. It also has a secondary effect of shedding any debris from the track surface.

In open wheel racing they go as far as to have pre-heating blankets for the tires.

Race tires needs a certain temperature to obtain proper traction on the tracks. below the needed temperature, The tires will just slide on turns or even at the straights if run cold. While going beyond the required temperature, the tires will blow out. You would notice at the pit areas, the tires are covered. Those are actually heaters to warm the tires before mounting it on their cars.

the tyres on a race car are one of the most important parts in how fast and how much traction that car has when accelerating or negotiating corners...but before that can happen the tyres have to reach ideal operating tempretature and that is achived by going fast,so when a racing car isnt going fast the ideal tepretature goes down and therefore maximum traction is lost...when you see racing cars weave from side to side behind the pace car is because they try to put as much friction on the tires as they can in order to keep them as close to optimal tempretature as possible

in a nut shell- the warmer the tires- the stickier-the better the grip

Side By Side Races

Warming the tires is the answer. Rarely this causes an additional problem when the driver accidentally swarves into another car.

When the tires cool down on cautions rubber will build up on them so by turning the wheel, the rubber can be rubbed off onto the track. Other times the driver is checking how tight or loose the car might be but mostly due to the rubber

They do this to warm up their tires. Tires are not at maximum grip when cold, so warming them up ensures better performance once the cars get the green flag.

The warm tires help them from spinning out on restart. spinning a tire or missing a gear on restart can cost them several car lengths.

They need to warm the tires up, because otherwise they'll lose traction which isn't really good for speed or handling while racing.

I have also asked the same question four times, and haven't got a good answer