It doesn't increase financial stability, it's a sign that you've achieved it. Though, a married man may seem more hirable to a company, since they can presume he needs the income to support not only himself, but his family.

According to Elizabeth Warren's book "The Two Income Trap", two income households are less financially stable because you've doubled the odds that someone in the household will become unemployed. Unless you live on one income and bank the other, having a lifestyle that depends on two incomes is less stable than depending on just one income. Of course, you don't have to be married to be a two income household and spouses who don't work outside the home exist but the default for married coupled does seem to be both work fulltime, which is financially less stable than having just one spouse working.