What vehicle, what engine, what carb?
Some carbs the secondary is vacuum operated - the Aisin on my Swift works like this ...
The accelerator linkage that opens/closes the primary prevents the secondary from opening until the primary is fully opened, and will close the seconday when the primary closes - but the secondary will never open unless there is sufficient vacuum.
Check the linkage on the secondary throttle plate - make sure it's not binding (I've had this happen), and make sure that whatever portion of the primary linkage that blocks the secondary from opening to soon is functional.