What is the basis for the idea that marriage requires a ceremony? Adam and Eve were never shown to have had a marriage ceremony, yet God commanded them to multiply. 

What is the basis for the idea that God requires a ceremony to be performed for marriage, rather than being a spiritual commitment made by the husband and wife?
The basis for a marriage ceremony is the elevation that it grants the parties. In Paul's day, for example, only the elite could actually &quot;marry&quot; in the sense we have today.  Sarah Ruden writes:

But for the polytheistic ancients, marriage was not as straightforward a matter. Slaves could not be legally married as free people were, but many had long-term unions that got some recognition, and raised their children together. Freedmen on average must have had less formal setups than the freeborn, since many of these setups started in slavery. In Latin the same slang, “tent-mate” and “shacking up” (literally, “tenting together”), could apply. For aristocratic Romans, the nobility’s separate legal history, along with large dowries, and ceremonies no one else went through, set their marriages apart. Even the Latin words for marriage, husband, and wife are not completely the same across different levels of privilege: uxor, for example, for “wife,” applies mainly to the upper classes; conjunx, on the other hand, can mean a wife, fiancée, concubine, or even animal’s mate, so of course it applies all over the place.

She continues by saying that marriage, as you define it, was more of an agreement than a ceremony.  She writes:

What is more, the ordinary type of Roman marriage was legally defined by consent to be married, which made getting a divorce easy for either party: a husband or wife had only to make known the wish not to be married anymore; and divorce, it appears, was common during the empire. A stricter type of marriage was available, but it was unpopular. This, then, was the array of committed sexual unions allowed among the Greeks and Romans.

Against this basis, she argues that for Paul, it was an elevation of the status of the individual that marriage would be &quot;held in high esteem by all&quot;

In 1 Corinthians 7 (see my discussion of Christian marriage in chapter 4 ) Paul lays down the law for Christians and gives his rationales— partly because, I think, existing laws and customs were too loose, yet nobody in this world had thought much about them.
Ruden, Sarah (2010-02-10). Paul Among the People: The Apostle Reinterpreted and Reimagined in His Own Time (Kindle Locations 355-367). The Doubleday Religious Publishing Group. Kindle Edition.