Your Standard Deduction (and personal exemptions in 2017) did not double.

If you made $18,000 in 2017 and claimed a $10,000 for the Standard Deduction and personal exemption, your income subject to tax was $8,000.
If you made $36,000 in 2018 and claimed a $12,000 Standard Deduction (there are no personal exemptions in 2018), your income subject to tax is $24,000.  

In that example, even though your income doubled, the amount of income subject to tax (after the Standard Deduction) tripled.

Does that make sense?

Yes. Thank you. Also, I have an old W-2 from 2016. I am still within the time frame to file for it. Should I file them together or separately?

You cannot add that 2016 W-2 into your 2018 return.  Each tax year has to be filed separately.

 If you need to prepare a return for 2015, 2016, or 2017 you can purchase and download desktop software to do it, then print, sign,  and mail the return(s)
<a rel="nofollow" target="_blank" href="https://turbotax.intuit.com/personal-taxes/past-years-products/">https://turbotax.intuit.com/persona...>
Remember to prepare your state return as well—if you live in a state that has a state income tax.
When you mail a tax return, you need to attach any documents showing tax withheld, such as your W-2’s or any 1099’s.  Use a mailing service that will track it, such as UPS or certified mail so you will know the IRS received the return.
Note:  The desktop software you need to prepare the prior year return must be installed/downloaded to a full PC or Mac.  It cannot be used on a mobile device.

We can't see your return and a refund is the product of many variables.  Compare your returns side by side to try to see what changed.