You're right, you don't understand, LOL.
Not to worry, from talking with people at work, people who understand taxes are a small minority.
My question is, do you owe taxes by April 15 or do you get a refund check?
You aren't paying taxes in your paycheck. The employer is withholding money to send to the IRS for taxes. When you file your taxes by April, that is when you find out what your taxes are. If it is less than you withheld, you get a refund. If more, you owe the difference.
When you say "filing married and zero" and "this year I filed single and zero" with the result of "My checks definitely feel smaller and comparing W-2s I've paid more taxes", that means your withholding changes. Think of the withholding as putting money away to pay for your tax and when you file, that is when you find out what your tax bill is.
Married couples pay less taxes together than 2 single people do. Thus, when you change your withholding from married to single, they will take more out of your paycheck because it is expected that your tax as single would be higher. Then when you file your taxes (which changing it now as you've said affects next year's taxes) you file married with your husband and you would together owe less than if you each were single so you've paid in more and get a larger refund (or owe less if not enough was taken out.)
Lots of people set up their withholding filing as "married at the single rate" so more comes out of the paycheck to get a larger refund when they file. It's sort of like a forced savings as they get huge refund checks. Most I know get in the realm of $8000 refund checks. They all tell me I'm doing something wrong because my refund checks were usually about $1000. They don't understand that the $7000 difference is in my paychecks. My checks were about $270 more than theirs (based on we all made about the same income.) Essentially by withholding "married at the single rate" and getting a huge refund, you are giving the government a no interest loan, to the tune of $7000 using my example here.
If you and your husband filed your taxes (the various 1040 forms or what you do when you go to an accountant/company) and both file single, you would have paid a lot more in taxes. Sounds like you don't file your own and go to an accountant and if so, they would have sorted it out for you. If you file yourself, you definitely want to file married with 2 dependents as you are both dependent (more dependents if you have children.)