The German word meinetwegen is used in several different contexts. Its first meaning can be translated as "on my account" or "for me" in English.

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Ich weiß, ihr seid nicht meinetwegen gekommen.

I know you haven't come because of me.

Caption 3, Verstehen Sie Spaß? - Sascha Grammel

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Hat Themba wirklich nur meinetwegen ein Eigentor gemacht?

Did Themba really score a goal against his own team just because of me?

Caption 33, Die Pfefferkörner - Eigentor - Part 6

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It can also mean "for example" or "assuming that":

Und wenn du dich jetzt meinetwegen dort auf die Seite drehst...

And if you now turn onto your side, for example...

Caption 63, Die Schmerzspezialisten - Diese Schlafposition solltest du unbedingt vermeiden!

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Additionally, meinetwegen can also suggest indifference, translated as "for all I care" or even the very rude "whatever" below. 

Machen Sie doch meinetwegen, was Sie wollen!

But do what you want, for all I care!

Caption 61, Märchen - Sagenhaft - Der Rattenfänger von Hameln

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„Meinetwegen“, brummte Frederick.

"Whatever," grumbled Frederick.

Caption 42, Piggeldy und Frederick - Unendlichkeit

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Von mir aus is a colloquial expression, and can be translated as "for all I care," "as far as I'm concerned," or even simply "I don't mind."

In welcher Form auch immer... bis morgen früh von mir aus.

In whichever form… till early morning, as far as I'm concerned.

Caption 45, Fastnacht - Karneval - Quartier Latin

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Von mir aus bleibe ich ewig

I don't mind remaining forever

Caption 7, Max Giesinger - Nicht so schnell

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Was meinst du? -Von mir aus.

What do you think? -I don't mind.

-Vielleicht hat hier jemand was gesehen.

-Maybe someone here saw something.

Caption 43, Die Pfefferkörner - Eigentor - Part 2

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Further Learning
Take a look for additional examples on Yabla German and try working on your own sentences with meinetwegen and responses with von mir aus. 

German has many French loan words or Gallicisms. Since an estimated 45% of English comes from French or Latin language sources, if you can learn to recognize words in your native English as having a French origin, there is a fair chance that these words are used in German. 

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In a previous lesson, we took a look at some more French-derived words in German that have the same or similar words in English. This week, let's discuss some German words that originated from the French but have different meanings than their similar English equivalents.

Die Frau bekommt ein Kind und ihr Chef weiß das.

The woman is going to have a child and her boss knows it.

Caption 9, Bundesrepublik Deutschland - Einbürgerungstest - Part 4

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In this case, the German der Chef and French chef can be a bit of a false friend of the English word "chef," since in English it means "the head cook" and not the more general term "the boss."

Bald waren sie bei einer Fabrik, bei einer Farbenfabrik.

Soon they were at a factory, at a paint factory.

Caption 6, Piggeldy und Frederick - Malen

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The German die Fabrik comes from the French fabrique, the -que ending having been Germanized to -ik. The pronunciation is nearly the same in both languages, with the emphasis on the second syllable.

Ich denke, er ist einfach eine komplexe Figur.

I think he is simply a complex character.

Caption 9, Dreharbeiten - zum Film „Playoff“

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The German die Figur comes from the French figure—like the English "figure"—and has similar meanings, but in most contexts the German is translated to "character" in English, making this a sort of false friend in most cases. Die Figur could, however, be translated to the English "figure" if you were discussing a geometric figure.

Bevor ihr einen Weihnachtsbaum aufstellt, geht am besten mal zum Friseur.

Before you set up a Christmas tree it's best that you go to the hairdresser.

Captions 17-18, Frohe Weihnachten - der Christbaum

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The German der Friseur / die Friseurin, from the French friseur, is rarely used in English anymore, and even the French tend to prefer to use the term coiffeur instead. The German also uses the term die Friseuse, but it is a pejorative. There is a secondary German spelling Frisör, but the German Duden dictionary recommends the -eur spelling!

Hast du die Gage?

Do you have the fee?

Caption 48, Verstehen Sie Spaß? - Sascha Grammel - Part 2

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The German die Gage and the French gage both pronounce the first G as a hard G and the second as a soft G. It might be incorrectly confused with the English "gauge."

Wenn du so viel Engagement in Mathematik aufbringst wie im Lösen von Kriminalfällen...

If you put as much effort into mathematics as into solving criminal cases...

Caption 36, Die Pfefferkörner - Gerüchteküche - Part 6

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Das Engagement, from the French engagement, has nothing to do with the English "engagement," which in German is usually translated as die Verlobung. 

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Further Learning
As a general rule, French words found in German are spelled the same, or nearly the same, as the French words found in English, but are pronounced in a German manner and written according to German grammatical rules—with nouns capitalized, for example. Take a look at this list of Gallicisms in German and go to Yabla German to find other real-world examples of the words used in videos.