Budgie is very likely feeling his oats as they say. The motions he's going through are typical self-stimulating actions that many parakeet owners find happen once the daylight hours get longer.
If you're positive he's a "he", the reason you might want to curb this is because depending on what objects he uses, he might hurt himself. Hard perches and some toys may irritate his tail area as he does his acrobactics.
He may also become more aggressive toward you, biting more (usually out of frustration) and territorial - enthusiastically protecting his area.
The bird in the mirror by the way, is (to him) the best looking, most perfect mate he could ever imagine!
If this is a 'girl' budgie, you might be facing egg laying and this is dangerous for many reasons, including overall calcium depletion in her body lending to health problems; but, moreso, the potential for egg binding (having one stuck inside) which can prove fatal in a matter of hours. There's no home treatment for this, a vet must be sought out no matter what time of day or night it happens.
To curb the behavior, change things up a little bit. Move the perches around, switch the food bowls with the water bowl, even moving the cage location a little can help.
Add some new toys, remove the mirrors and make doubly sure you're feeding right.
So much information is flooding the net these days about what to feed a companion bird, whether a budgie/parakeet, cockatiel or marvelous macaw, it's sometimes difficult to wade through the junk science, old wives tales, well meaning owner advice or just plain dangerous suggestions.
It's generally recommended that most of today's companion birds have a predominantly pelleted diet. Pellets have been continually updated since being introduced to the market years ago and today's formulas are better than ever.
Supplementing this diet with fresh foods every day is ideal and many owners find they can re-introduce seeds - in limited amounts (perhaps once or twice a week) without the bird refusing the pellets overall.
http://www.cockatiels.org/articles/nutrition/diet.html cites feeding both seed and pellets, but only after weaning the bird from a mostly seed diet.
http://www.letstalkbirds.com/cockatiels.htm
Here is more on ideal nutritional needs:
The American Cockatiel Society http://www.acstiels.com/Articles/BasicCare/cockatie.htm
The Bird Care Library at Harmony Animal Hospital http://www.petvets.com/petcare/birds.html#nutrition
Finally, level out his sleep time. 12 hours daylight, 12 hours nighttime = one happy, healthy bird!
This can be accomplished by moving the cage to another room or providing a separate sleep cage in a room with subdued light and low noise. Eventually, 12 hours + 12 hours year ‘round may be enough. If moving a cage isn't possible, covering it and lowering the noise level in that room (as we'd respect that anyone in the house might be sleeping) is helpful. We don't care for complete cage covering since most birds need to be able to see out for reassurance that they are safe and for reasons of air circulation, so we cover all except about ½ of the front half of the cage (vertically).
It's very important that the cage get uncovered or the bird be taken out of their nighttime room/cage at the same time every morning. This does mean that you will not be sleeping in on weekends or holidays. You have to get up and start the bird's day as usual (and if you really want to go back to bed, go ahead).
Board Certified Avian specialist Dr. Theresa Lightfoot suggests that longer ‘nighttimes' 14 hours as opposed to 12, may help in stubborn cases of mating behavior .
Now you've got a lot more to go on and hopefully keep the gregarious, friendly personality while losing the 'weird' body language.
Good luck!
Certified Avian Specialist
Cert. Avian Specialist; Int. Assoc.Animal Behavior Consult; Pet Ind. Joint Advisory Council; author