“offer”

To hold out or put forward something for acceptance.

“She proffered her hand across the table before he could speak.”

Best for: Slightly formal writing or dialogue; adds quiet elegance to a simple gesture.

To formally present or put forward something for consideration or acceptance.

“He tendered his resignation with a calmness that unnerved the room.”

Best for: Business, legal, or formal contexts; carries a sense of ceremony and weight.

To put something forward toward another as a gesture of goodwill or invitation.

“The city extended an olive branch to the striking workers before dawn.”

Best for: Works well when the offer carries warmth or diplomacy; slightly figurative.

To condescend to grant or bestow something as a gracious concession.

“He would not vouchsafe even a glance at the petition laid before him.”

Best for: Literary and historical prose; implies the giver holds power or privilege.

To supply, furnish, or make available something for others' use or benefit.

“The inn had purveyed comfort and strong ale to travelers for three centuries.”

Best for: Best in literary or atmospheric writing; evokes an older, richer world.

To offer up or surrender something, especially by renouncing it for another's benefit.

“He abnegated his share of the inheritance, pressing it into his sister's hands.”

Best for: Rare and striking; use when the offering involves self-denial or sacrifice.