What kind of nuance does 呗 have? In the northeastern dialect, 呗 is sometimes added to the end of a sentence. Although I use it often as well, I don't really know how to explain why it is used and what nuance does it carry.

My first thought was that it is used to state something obvious, like in this example (assume A has never seen a TV):


  A: 那是啥呀？ (pointing to a TV) What is that?
  
  B: 电视呗。 A TV (of course).


But then I thought I was wrong because when you ask for favours you can also use 呗, like this:


  你帮我把这个整完呗。 Help me finish this.


And I found nothing "obvious" in that sentence.

so I think it is not always to state something obvious. What nuance does it carry exactly? Or in other words, how can I explain this to a foreigner?
From 汉语大词典

呗 II  
bei  
˙ㄅㄟ

1. 助词。表示事实或道理明显，易于了解。  
▶ 何永鳌《火焰山上四十天》：「有什么奇怪的，一块红石头呗。」

2. 助词。表示勉强同意或无所谓的语气。  
▶ 周立波《暴风骤雨》第一部一：「他想，不明白就不明白吧，反正他们会给他车钱，这就得了呗。」  
▶ 草明《乘风破浪》第四章：「他闷闷不乐，低着头说：‘挺好呗。’」


So, the 呗 in your first example is the first meaning above.

But I think in the second one, 呗 may mean 吧.
你帮我把这个整完吧。