Grammar: meaning of nanda yo ne/nandesu yo ne

For a very long time, I've been wondering what it means when Japanese people end their sentences with 〜なんだよね or 〜なんですよね.
One example I can think of off the top of my head is if I ask someone if they're free to meet, and they then respond with　バイトなんですよねー.

What would the equivalent be in English in terms of tonality or sentence structure? And what would be the difference between なんだよね and なんだね ?

If you put this なんだよね into polite speech, it would be なんですよね

If someone asked you you have time to meet that evening and if you said:
バイトです。

it would sound a bit... too blunt. You go a bit roundabout and say
バイトなんです (It's that I have some part-time work.)
バイトなんですよね (It's that I have some part-time work. So, you know...)
and leave that someone to understand that that's the reason/background, and therefore the answer is no, you cannot meet up. (The "...desu yo ne..." ending is more prevalent among younger people.)

This "...n desu" (or "...no desu") construction appears in textbooks as a way to state a reason, or explain the situation, in a somewhat indirect/polite way.

なんだよね (or なんですよね) is used as above, and なんだね (or なんですね) would be used to ask a question in a confirming way, but can you give a whole sentence for the second one?

I'd like to but ...
And
A so, I see you are working, etc...(that is why you can not meet up, etc.).

Hi, and sorry for my tardy reply.

So, baito desu would sound too blunt? Well, I can tell you right now that some Japanese people have answered me like this before. They must not have been very interested to meet me at all...

I understand what nandesu yo ne means a lot better now. I had a feeling it meant something like that but couldn't put it into words the way you did, AK, so thanks.

As for your question, sorry if I was not clear. I just meant, what is the difference between バイトなんですよねー and バイトなんですねー, but I guess there's not that much of a difference judging by your explanation.

If you ask "what is your plan after this?" or "any plan for the evening?" and then that person might answer "Baito desu." This is very plain way to answer. And even if you asked if you can meet later, if that person was in a hurry or in a "work mode" already, so to say, then that answer is well possible, though not the most polite way to answer :)

About the last part, there's a bit more to it. バイトなんですね〜 would be "Oh, so you have part-time job, I see (unfortunately!)" kind of question/confirming what the other has said. So (it might sound quite lame, but) the conversation might go like this:

-　きょう　ゆうがた　あえますか？
-　バイトなんですよね〜
-　ああ、バイトなんですね〜。

- Can I see you this evening?
- Um, (I can't, because) I've got some part-time job to go to, you see.
- Oh, so you have part-time job to do, I see (sad as it is, I give up then).

Thanks for the clarifications, AK (thumbds up).