Your button with the eagle appears to be an "early" version of the US Army eagle-button. (On the "early" versions, the eagle is shown "leaning" toward its left side.) If your is a 1-piece brass button (the loop was attached directly onto the rear of the button's front), it is from the 1820s through late 1830s. If your "leaning eagle" button is a 2-piece button (the loop was attached to a disc of brass in the back of the button), it is from the late-1830s through 1853.
Would you be the honest seller I recently communicated with on Ebay, and whom I invited to join this forum?
Regards,
Pete