Welcome = You're welcome?

The meaning of welcome varies greatly depending on the context.

Welcome =  Thanks for coming

Used alone, welcome means "I'm glad you came."  Welcome to our home. In this case, the answer is usually "Thank you." But welcome can be used in other ways.  A welcome change is a change that someone wants, a change that is welcome.  At many resorts, patrons are offered a "welcome drink" on arrival.   Welcome can also be used as a verb.  I welcomed him to our meeting = I thanked him for coming to our meeting.   The opposite of welcome is, as you might expect, unwelcome.  The news that John had just lost his job was unwelcome.   A welcome mat is a rubber rectangle outside your front door with the word "Welcome" on it. Its main purpose is to provide a place to clean the sole of your shoes.  If I say "The welcome mat is always out", the person I'm talking to or about is always welcome to visit me.

Welcome to the verb or noun

When we offer to let someone do or have something, we can use welcome to. You're welcome to spend the night here. Feel free to spend the night here. Spend the night here if you want. I do not want this shirt anymore. You're welcome to it. You can have it.

The difference between these two meanings of welcome can occasionally give rise to ironic comments, which may not always be, er, welcome. A: Welcome to Texas! B: You're welcome to it! (That is, You can have it!)  B is clearly not very excited about the state of Texas.

You're welcome - the response to "Thank you"

You're welcome is the preferred response to "Thank you", at least in North America A: Thanks for your help. B: You're welcome. Other less frequent responses include (It's) my pleasure and No problem. Sometimes No problem is reduced to "No prob".  A: Thanks for the help, buddy. B: In prob, man.  In the UK, we hear other answers: Do not mention it and Not at all. In Australia, "No worries" is apparently a popular rejoinder to "Thank you".

Thanks for reading!