Profile view doesn't display the thumbnail, but displays the full image. It can do so up to a maximum of 25% of the available space in the canvas header; this can't be changed without extensive CSS work. If the available space is the issue then you've the component view of your site too small.

Within CB > Configuration > Images ensure your upload sizes are set appropriately. Be sure to also check the sizes of the avatar field it self in CB > Field Management. Note changing the sizes at either locations has no impact on already uploaded images.

It doesn't look like you're using the canvas layout completely so you're better off just moving the tab the avatar is on to a different tab position instead of using the canvas positions.

Do not use the canvas positions if you are not going to use the canvas layout. All positions prefixed with "Canvas" are part of the canvas layout. The canvas layout displays avatars perfectly fine on mobile. You can check this for your self on our demo site below.

demo.cbdemosites.com/profiles/susan

They can not get any larger if you are using the canvas layout. That is how it is designed. You would need to completely override its CSS to give the avatar more room as its container has limited space.