Hi guys, my rock hopper's rear wheel has this weird up and down wobble when I spin it freely. It makes the whole bike go up and down like there's a weight at a curtain point in the tire/wheel.

It's not left and right ( no need for truing)

There are multiple aspects to truing a wheel,
lateral true (left and right as you put it)
and radial true -how centered the rim is to the hub, 'up and down' evenness

Sounds like yours needs adjustment to radial true

also possible that you've hit something and it is a dent in the rim that you are feeling; which may mean a new rim is needed

How does it ride?

A bicycle is designed for riding, not for spinning the wheels freely. If it rides OK then it's not broken and you'll continue to be OK unless you try to fix it.

A few things to check...is the tire seated properly? Does the tire have a bulge? Is the rim bent? Or is it out of round? All of them might be correctable or you may need a new rim or tire.

Aaron

xenologer et al., the topic is unevenly weighted wheels, not vertical truing, dented rims, etc.

wasabiboi, almost all rear bike wheels exhibit that same jerking when spun up to speed on a work stand, which is where you noticed it, I imagine. Doesn't affect the ride, or you'd have noticed it before, as Retro Grouch said.

If it bothers you, add reflectors or other items to the spokes opposite the valve stem or rim seam, as the case may be.

It wobbles up and down...that can be a weight issue or an out of round issue, weight issue? You can determine if it is tire, tube or wheel. Rotate the heavy sides opposite each other, unless is is affecting bike handling most cyclists don't get going fast enough for that to have much effect on the bike.

Aaron

Are you using slime inner tubes? The slime can run down and collect when the bike is sitting and in cold weather it won't spin out when the tire is rotated. The slime ball makes the wheel out of balance and hops in the stand.

An amateur with a spoke wrench can put a hop in a wheel quite easily.

I have to admit I was guilty of that when initially trying to true a wheel of unknown history while still on the bike.
I didn't realize the rim was "splayed out" from hitting a curb or whatever.
I kept trying to "pull" the far side to the center, spin the wheel and look for the next "high spot".
It turned out to be opposite of the spokes I just "pulled". After going back & forth a few times, I ran out of threads!

I've since bought a truing stand and keep a caliper handy to measure "suspect" areas to compare to the rim width in general.
IF you remove the tire, you can use an adjustable wrench as a gauge an slide it around the rim to check for "tight" spots.

This is true too...

I have a wheel on a Dahon Classic that just rolled in, had a hop in it, the stock rims on that bike are very, very low end. One had a 5 mm spread in the rim that was causing a noticeable hop. After measuring with a caliper, a bit of judicious hammer work it is a lot closer to round and the hop is all but gone. These are chrome plated steel rims, alloy rims are not nearly as forgiving to being beat back into shape. YMMV...

Aaron