Growing up I heard it was so if need be you could swing them as a weapon at the end of the belt. I even heard soldiers would melt bullets to add more lead to their buckle to make it a better weapon.
A weight on a short cord, called a Slung Shot was a familiar weapon in the US at the time. Abraham Lincoln's most famous trial was defending a man against a charge of murdering another with a slungshot.
To clarify: the idea was not that the Cavalry, at the start of a battle, would fling aside their guns and swords, strip off their belts and charge in swinging belts over their heads. It was that Cavalry and Infantry both can find themselves fighting hand to hand with ammunition gone, rifle stock or sword shattered, and no bayonet in sight---and no longer having a live horse. There was a very common idea among draft age men in the Vietnam war era that in hand to hand combat you will use anything that would hurt if it hit someone. And I can tell you that getting hit in the head with a fast moving lead weighted US belt buckle would hurt--though I do not know if it ever actually was a practical battle field last resort.
I have changed the title to reflect the fact that these were not only Cavalry equipment. To judge by pictures on line today they were not even primarily Cavalry. You see them far more often on Infantry.
@AllInOne asked for links showing they were filled with lead. A Google search of
cavalry plate "filled with lead"
will show it is common knowledge. Dealers routinely say things like
The reverse has 100% of the lead fill with both arrow hooks and tongue
to show the item is in good condition and to argue for authenticity. This comes from Military Accoutrements.
But in case you only trust Congressional documents from the era you can see
sword belt plates (brass, filled with lead)
Listed in the Kansas Veteran Association and many similar inventories.
The discussion at Reenactor's Forum and FC Sutler convinces me that @user2448131 is right. The lead was was a quick cheap way to hold the attachment hooks on. It is not for strength: thick sheet brass is plenty strong for a belt buckle let alone a box plate, and lead is not strong.
As to whether soldiers ever did swing it as a weapon -- or thought they might do that -- I'll wait for historic evidence or at least someone who knows what hand to hand fighting is.