I've got a very similar decision. We will soon have a 2.75% 15 year mortgage that we could pay off in about a year and a half once we sell our old house, if we put our minds to it. Or we could sell stock and pay it off now.
My wife and I REALLY REALLY REALLY like not having a mortgage payment. It feels like freedom!
That said, let's look at some numbers.
You owe $125,000 and pay $300, or $3600 a year in interest. That amount of interest will go down each year.
Let's pretend that your $125,000 investment returns 2.65% like clockwork. It would make $3,312.50 a year for you.
You would be 287.50 in the hole on interest the first year, and progressively less each year.
Now, if that $125,000 was making 6%, it would be returning $7,500 a year. Your interest cost would be free and you could re-invest the difference, pay down the principal, or use it for a monthly mortgage payment.
If you re-invested the $3,900 surplus you would have a house payment nest egg of $128,900 invested. A 2.65% return next year would get you $3,415 and change, almost as much as your new, lower interest payment for the year.
A 6% return would get you $7,734. You interest payments are covered and you have the same choices with the surplus as before.
What could go wrong?
Well, stocks could dive 50% and stay there for 3 or 4 years. Your % income would be similarly affected.
If you had to sell a lot of stock to pay your mortgage payments for the year, that would hurt.
However, if you could cover your mortgage thru that kind of downturn for a few years, then it's a slam dunk not to pay off the mortgage. If things are too tight for you to do that, then maybe another decision is more appropriate.
If it would be too painful to make mortgage payments in that kind of downturn (and remember, in that kind of downturn, it's hard to find any work, especially if you're older), I would consider paying it off. It takes a lot more invested money to cover the full cost of housing than it would to just pay it off.
For now, we're deciding not to pay off our mortgage early. We're going to invest the money instead. (We've decided we'll probably rent out the old house for a couple of years until we're ready to buy more rentals that would provide a better return. We'll sell it then. We're still researching rental and sales prices to make our choice.)
Best of luck!