Me and you, we get along,
Sometimes I will start a song.
I'm quite average you say,
Showing money through the day.
I'm not from here, rather old.
Sometimes very small I'm told.
I tug you and pull you near,
Mutter now, who am I dear?
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1$\begingroup$ If not for the line 'showing money through the day' I would have guessed a mobile phone. $\endgroup$– rhsquaredJul 20 '16 at 15:31
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Are you:
μ?
Me and you, we get along,
μ and u looks alike?
Sometimes I will start a song.
I'm quite average you say,
Symbol for 'mean' in statistic
Showing money through the day.
µ means the Stock Market's portfolio?
Edit: NASDAQ:MU (answer from OP)
I'm not from here, rather old.
μ is the 12th letter of the Greek alphabet
Sometimes very small I'm told.
it represent greek small letter me (probably wrong)
Edit: μ means Micro : 10-6 (credit to Moose)
I tug you and pull you near,
Google and found µTugs
Edit: μ means Magnetic permeability (credit to tmpearce)
Mutter now, who am I dear?
µ! µµµµµµ
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2$\begingroup$ Mu is the metric prefix for micro, which is one millionth of the base $\endgroup$– MooseJul 20 '16 at 23:18
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1$\begingroup$ You've got it. See if you can find some items that are better related on money, small, and tugs. The money might be tough. $\endgroup$ Jul 20 '16 at 23:20
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$\begingroup$ A couple of ideas: for money, mu could represent microloans; for tugs, muons have electric charge and also much more mass than an electron, so could exert more force on other objects... And I agree with Moose, mu=micro=10^-6 is the answer for "small" $\endgroup$– tmpearceJul 21 '16 at 2:01
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1$\begingroup$ @Alex The money one was a bit of a stretch. I was thinking along the lines of google.com/finance?cid=12441984. Great job! $\endgroup$ Jul 21 '16 at 14:36
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Are you
the Sun?
Me and you, we get along,
Yep, the Sun is good.
Sometimes I will start a song.
"Sunshine on my shoulders makes me happy..."
I'm quite average you say,
The sun is an average-sized star.
Showing money through the day.
The golden sunshine?
I'm not from here, rather old.
The Sun is 4.6 billion years old, and due to ~5 billions years of astronomical movement, was likely formed far away from "here" (wherever that is).
Sometimes very small I'm told.
The sun is small compared to some stars. It's also somewhat 'small' from our vantage point.
I tug you and pull you near,
Gravity.
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$\begingroup$ +1 for some good thoughts, but no. The first line has a hidden clue, and unfortunately sunburns make me not get along with the sun. $\endgroup$ Jul 20 '16 at 20:24