Looking for lightweight bulpup

The Akela is about $130 over your budget so I would seriously consider one of KatoKevins Flashpups. Not sure if his are .22’s but with the limited air capacity, I’m not sure what a .25’s shot string and count looks like. But those guns are about as good as you are going to get with a sub $500 budget. You could also seek out a used Puncher Breaker. The P15 is the king of lightweight bullpups. It’s also king poop of turd island. I have one and have over $1,300 in it to get it up to other bullpups standards. It was the most extensive project gun I ever owned but it’s a keeper now.
 
I really think you should consider a used FX wildcat MK2 if your budget could go up. What fine rifles these are! Love them for pellets. I am always surprised how light mine is with 6 full magazines on the side of it, wearing a Hawke Frontier 3-15x50 and yet it's still a feather. Obviously if it can't my suggestion is pointless, just throwing it out there. Keep checking the classifieds as you can substantially increase your airgun value with $500 with the right deal and seller. 
 
22cal FlashPup.2&1/2 years now. Solid performer. Hard hitting and very accurate out to 50yds with good pellets like JSB 18gr/AirArms 18gr/and H&N Match 21gr. Only issue I had were with the magazines. It comes with a single shot tray that I use exclusively. I have to be more aware of rifle cant but that could just be me. Steve of AEAC did a review as well as Shooter 1721