Newbie needs a new airgun

It's going to be tough getting into a PCP air rifle for $500 because you need other items in addition to the riffle to start shooting it which costs more money. But PCP's are a joy to shoot and easier to shoot well because of the almost non existent recoil. You'd need to buy a high pressure pump, or a scuba type tank, and or a high pressure compressor. Also maybe a fill adapter to fill from the tank to the reservoir on the PCP airgun. 

Your Kodiak is known as a "springer", it's a spring piston air rifle.Your rifle "might" be accurate with higher quality pellets such as JSB brand. I'd try that first. Also it's important to place "everything" that touches the rifle the same way every time if you want consistent accuracy. Those Kodiaks are not easy to shoot because of it's violent power.

Possible your barrel is leaded up, scope mount or rings are loose, as well as the screws holding the action to the stock. Check it all.

Michael, you should start a sticky on this subject.
 
If you only need a birdie gun to shoot pest. I say stick to break barrel and multi pumps. Once you get into the dark side of pcp. Your $500 budget will become $5000. You can do with a cheap $300 PCP and a cheap $40 hand pump. But soon it will be a daystate, edgun, fx, brocock.,etc and those guns alone is in the thousands of dollars. And then tanks and high pressure compressor. Fittings and filters. Pcp ain't cheap. Just an advice.
 
Seneca Aspen. You can get one at PA. for $400 with an AO scope included. I am suggesting this because of your budget. You could also get a Diana Stormrider for $200 and pay $250 for a Yong Heng air pump on Ebay and another $75 to $100 for a budget scope like a UTG. There are several options which are out there but if I had to pick one in your budget and weight criteria it would be the Gen 2 Stormrider and the Yong Heng pump. Welcome Aboard and best wishes in your search. One thing I recommend is you run your ideas by the members before making a purchase because there are many vendors who give discounts if you know which ones do and the coupon code. Crosman for instance gives a 25% discount with the code AGNATION and if you buy on Friday and your purchase is $150 you get free shipping. The main reason I suggested the Stormrider is the fact that they are very light weight for a pcp.
 
How about a .177 refurbished Hatsan Airtact for about $50 delivered?

https://hatsanairgunsusa.com/

Go to products then refurbished, bottom of first page.

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I recommend the Weihrauch HW50 from Airguns of Arizona. Much lighter than what you have now and it cocks with less effort. Super accurate German barrel on a mid size springer.

If your with driving distance of Gilbert, drive over there and they would probably let you try one. https://www.airgunsofarizona.com/spring-piston/weihrauch-hw50s-air-rifle/

If your eyes are getting older, as mine are, A 4-16 x 50 scope is nice.