Does wearing a backpack weaken your jumping technique?

You have more control over weight on you than on the bike, so long as the pack is fitted nicely and doesn't bounce around too much. This doesn't just apply to jumps but all the time, as your bodyweight is part of your control but weight on the bike is passive. Imagine rolling over a tree root on a hardtail or even rigid forks. Weight attached the bike must lift over the frame, but if you're off the saddle and riding properly your body and backpack float over the obstacle, barely rising.

Moving a few kg/10-20lbs between frame and body is noticeable. I'm a perpetual mountain bike novice but ride a lot on road. On the MTB (hardtail) I either use a hydration pack similar to you, or copy my road kit: a litre bottle of water, tool bottle in a 2nd cage, and saddlebag on the bike. Even at my level (no big jumps, but the effect holds even for bunny-hops) bike handling is easier with the weight on my back, though it's fatiguing on a very long ride. This makes sense. When your weight is on your feet and hands rather than your saddle (i.e. most of the time when riding technically) your bodyweight is sprung on your legs - so is the backpack. When you jump, you launch your body into the air and the bike follows you. You launch a backpack with you, but extra weight on the bike has to follow you.

You tagged “dirt jumping” in the question. At a jump park, I would definitely remove the backpack. At the very least, you won’t risk blowing up the water bag or breaking a tool in the (inevitable) event of a crash.

For normal trail riding, it goes either way. Some people prefer the backpack, others prefer the on-bike solution. It’s really all up to you. It’s best to pick one solution and stick to it though; as you described, the difference in weight balance really does mess with your skills and technique.

If you want to carry stuff on the bike, it is common to use normal bottles and cages for water. Tools and supplies would normally be held with elastic or Velcro straps. Contrary to what Chris suggested, I would not recommend the use of a saddle bag: they flop around all over the place and sound like your bike is falling apart. They also make it harder to use a dropper post.

A fanny pack is a common solution where I live: water goes in a bottle and cage, bike tools go in Velcro straps, and soft goods (keys, phone, snacks...) go in the fanny pack. You can pick a variety of sizes of fanny packs to suit your needs.

Indeed, the longer the ride, the better prepared you must be. The further away from help your ride takes you, the more situations you must prepare for.

As a mountain bike rider who does XC (kind of), and Downhill, but also an urban rider / commuter and have made a couple long road trips, I use all modes of supply carrying, according to situation.

For XC riding, either short or long rides I use a backpack. A small one for short rides, a large one for long rides. Mostly for food. Tool kit is the same.

My definition of XC may not fit the "official" ones. I include in that some very long rides where the goal is "just get there" enjoying the scenery, aggressive training sessions focused on endurance and more playful rides focusing on practicing skills and drills. These last ones are the ones that include jumping and other stuff.

I classify the rides because that allows me to focus and prepare better for what I'll be doing, choose the right apparel and thus make my rides more enjoyable. Not all rides have to have it all.

When I want to have fun jumping and practicing skills, I choose shorter routes so in case or bike breakage or injury I'm closer to help, closer to my car or home. Small backpack. Only essential tools and just enough water and food. Since que ride's goal is not distance, I'm willing to, for example, make two loops or more on a circuit, stopping for rest and replenishing on each loop.

On the other hand, when the ride is a long travel across a mountain where I'd be far away from any help and possibly across areas with no cellular coverage and maybe not accessible for a car, then I'd go as prepared as reasonably. Extra tools, extra water, extra food, but Also, my riding becomes focused on "getting there", avoiding risky situations and difficult maneuvers. On those rides I enjoy the descents but do not race downward, keeping a good headroom inside my skill level and not trying to compete with fellow riders.

So this is my suggestion: have different types of ride and focus on different types of activities on each day. That will allow you to optimize the ride, your time and the toolkit. Even you ride companion may be different one day from another. That may even prove beneficial for your skills, strength and fitness level.

Regarding other types if riding I do:

For DH I have either used the backpack or ZERO carrying, as DH is often practiced using some form of shuttle service (usually a friend's car). I normally leave my supplier in that vehicle and I hydrate and eat while riding the shuttle up. For the descent I want to be as free as possible and I'm already covered in protective gear. I have used the backpack when riding alone and not having a shuttle, but it interferes too much with the other protective gear so I don't do that much often.

EDIT: (I forgot to address the question in the title). I do not think using a backpack would "weaken" your technique, but it sure does alter it, either for good or for bad (most likely the second). In general riding, a couple of jumps with a small to medium backpack, well strapped to your body won't do much harm. But for freeriding and acrobatic jumping it would indeed hamper your ability. Jumping and acrobatic rely a lot on muscular memory. If you have to take care of your backpack's position and movement all the time, you will teach yourself to also be controlling it, along with your bike and body. That's why you feel awkward when jumping without it: surely you are performing micro movements that are no longer necessary when not wearing the b.p. Somehow you must feel some thing that you do during the jump does not make an effect, or feel that you must be doing something you aren't.

As I said, the times I used a b.p. for DH riding I could not tackle the usual obstacles in the same manner, I had to prepare differently and felt that I had to make nothing but a perfect takeoff.

Another aspect of it is safety: an object inside a backpack may move during jumps if not properly restrained and cause severe injury in case of a fall. A loose tool may and up positioned in such way that in an accident may protrude outside its pocket and insert into someone's body. If you are carrying tools while jumping, ensure they are properly held in place and that all sharp edges and pointy ends are covered and tucked in.

End of edit.

For commuting I either use a backpack or some bag + rack combo, in order to be able to remove "everything" from the bike and lock it on the street. The backpack is the most agile in this regard, the rack is the most comfortable as the bike bears the load and the body is free (helps with cooling). The only thing I carry attached to the bike is the lock.

For long road rides, I use a rack and 3 water bottle cages. Everything goes on the bike. (I'm not a tourer, but that's where I take the idea from and it pays off)