"Welcome" can be a verb, and is then used accordingly:
I welcome you to my house.
I will always welcome her.
He welcomed me to his party.
But it can also be an adjective:
You are welcome in my house.
She is always welcome.
I was welcome at his party.
She made me feel welcome.
The break was a welcome relief from the hard work.
It can even be a noun:
I gave him a very warm welcome to my house.
Sometimes, you can use similar but slightly different constructions, but the meaning of your sentence will change:
I was welcome at his party.
I was welcomed at his party.
The first simply means that I was invited, or at least, my presence was appreciated, at his party.
The second version indicates that someone actually bade me welcome when I arrived at the party.
To include the examples from the OP:
I am obviously not welcome here.
My presence here is obviously not appreciated. Whatever the reason, people would be happier if I did would not be here or come here.
I am obviously not welcomed here.
I might as such be welcome here, I might have an invitation to this party, but as you can see, obviously nobody is standing at the door to welcome me.
(I guess I'll just sneak in and get a beer.)