Here is the Federal law that applies when States do not have their own rules or if you are outside State waters (offshore)
NEW FEDERAL LIFE JACKET RULE
The United States Coast Guard's Life Jacket Rule for Children went into effect December 23, 2002. In support of the ongoing efforts of the states and Coast Guard to improve boating safety, the Coast Guard is requiring that all children under 13 years of age wear Coast Guard approved life jackets, while aboard recreational vessels underway, except when the children are below decks or in an enclosed cabin.
This rule was created to address the problem of childhood drownings while boating. Between 1995 - 2001, 210 of our children, under the age of 13 died while boating. One hundred and twenty one (121) of them by drowning. Most of these deaths could have been prevented if the child had been wearing a properly fitting life jacket.
The Rule affects only those States that have not established requirements, by statute or rule, for children to wear life jackets. For the remaining states, the rule recognizes and adopts the existing state regulation, even if it is less stringent.
Penalties for a boat operator who fails to have all children under the age of 13 wear a life jacket are similar to those for failing to have life jackets on board. Penalties may be assessed up to a maximum of $1,100 for each violation.
Interestingly, I had a hard time finding the new USCG rules even on their website. The USCG rule is a better one, yet defers to State rules regardless of how lax they may be.