Many bills (like utilities) often have a base component and a variable component, you pay only one base component if you live in the same house.
Rents for two studio apartments are greater than the rents for a single bedroom apartment, two one bedroom apartments go for more than one 2 bedroom apartment. A chunk of that is the shared square footage of bathrooms, kitchen, Etc.
Food costs in bulk are lower than food costs in single serving quantities. It is more cost effective to cook for two than it is to cook for one (save on energy costs and food)
Yes, being married (not having kids), will give you access to more money than you would have if you remain single.
There should also be a secondary effect on savings (if they were combined) where the compounding of interest would work more effectively on a larger principle.
Things like health and car insurance can cost less for a married couple than they do for two individuals, especially if your state doesn't have a domestic partnership law.
Stuff like that can add up surprisingly quickly.
Lower insurance rates (home, auto)
(usually) lower health insurance rates (family plan rather than two single plans). My company doesn't even charge a premium for putting your non-working spouse on your plan.
(usually) Tax benefits
Get married in a courthouse around the end of the year, before the year of your wedding. The following year, have your ceremony. You extend your Married Filing Jointly status to the previous year you were going to originally take credit for it.
That's my best guess though, and depends on your incomes.