You have all the rights you had on the first day of marriage. In other words, you do not gain additional rights as time passes.
If you were to get divorced, a judge will consider the length of your marriage among many other factors when deciding on alimony. Also, to be eligible for some types of social security benefits from your spouse if your spouse passes away, you must have been married for 10 years.
The main "right" you have as a husband or wife is that you own half of all property and income acquired by either of you after you were married (bank accounts, real estate, etc.). This is true starting from the day you get married -- there is no waiting period.

