General Lee SWR

Hello everyone I recently got a General Lee, converted, peaked and tuned by reputable shop when I purchased it.18ft Wilson coax, 4ft Wilson top load tunable antenna. On low power (around 1.5 dead key) the SWRs are 1.2 on 1 and 1.5 on 40 but on high power (round 10 dead key) they are 2.5 on 1 and 3 on 40. Using cheap Astatic SWR meter got from truck stop. Prior to the general Lee I used peaked tuned cobra 29 (around 7 deadkey) and swr were same as low power on the GL. Why is my SWR higher on high power?
Any advice or redirection is appreciated!

 

Yes, i turned the little knob on the side all the way back. And the needle in the meter is SUPER sensitive when on high power
I'm fairly new to the CB hobby, always used a cobra 29, this is first big radio I've had

 

Also I've read that the actually SWR doesn't change with power, just the meter does, and I've also read the exact opposite. I don't know which to believe. And CB shop is kinda far I hardly get time to go to it so I appreciate the input and advice

 

Stargazer
CB key and knife
XT 160 GA I-85

 

So I should trust my low power SWR reading? Since it was the same on my old radio? And possibly that meter isn't made for testing a 10watt deadkey since it's a standard CB meter expecting 4watt or less?