a6500 vs a7ii

I am planning to travel to Asia (South Korea, Hong Kong, Macau, Japan). I am not sure what's the better body to travel with. Just need something a lot lighter than my Canon 5D Mark 3 and Sigma 50mm 1/4 Art.
I have a budget for roughly $1300-1400 body only. And roughly $600-800 on lens.
I am planning to shoot landscape and street photograph. 4k is a optional thing, but not required since 1080p still looks great.

I'd say the a6300 + 16-70/4 lens.

It depends on what you want to use the new camera for. Are you going to keep your Canon system or planning to move to the Sony system? I have the A6000 and I am very happy with the image quality I get out of it (which of course depends on the lens you put in front of it too). From what I have read around A6300 and A6500 are only marginal improvements over A6000 in terms of sensor performance. So I am in the middle of transition to the full frame system which I have longed for since a long time ago.

For me, I am going to be keeping my canon lenses and I would like to adapt my lenses to the next body I am going to be using.

Either the a6300 or a6500 for what you describe you want. I went with the a6500 for the buffer and IBIS. If you want some cheap, but good picture quality lenses, get the Sigma 19, 30, and 60mm f/2.8. They are all under $200 each and are great.
I use the Sigma MC-11 adapter for my Canon lenses. All of mine work great with it. Good luck!