I have no beliefs. There are numerous things that I cannot see but of whose existence I know.

I can't see my brain either. And I can't tell if it exists?

You can't see electricity. But I'll show you how to prove its there.

I try to place belief first in the things that have the strongest evidence, and things which have the weakest evidence, last. Seeing is just one source of evidence.

But you have to be more wary of evidence that has been given to you by other agents. For example, if I see dead animals and cat droppings in my garden, I am reasonably certain that next doors cat has been in the garden. But if an irate neighbour tells me that they are fed up with the cat leaving shit in their garden, I wonder. Does he know the difference between cat droppings and fox?

First, let's assume that by 'belief in' you didn't intend to make this an 'article of faith,' and what you really meant to say was 'accept,' as in, 'accept a fact.' Agreed? If so, knowing that, in addition to our capacity to reason, we have 5 senses, why would we limit our acceptance of a fact only to that which we can see?

I like to decide on a case-by-case basis.

Depends are we talking oxygen or gods???

Sight is only one method of detecting evidence.

Yes I do but I'm more comfortable when I either see something or have it explained thoroughly.

Absolutely not. I don't believe IN anything.

Gravity, atoms and subatomic particles , far galaxies etc

Air, electricity, electrostatic and electromagnetic fields, magnetism, gravity. I might not be able to see them but I believe in them because I can see, and reliably predict, their effects.