You lose leverage the second they know you’d accept anything.

Leverage is not attitude, it is the real chance that you walk away. The moment someone is certain you would take any version of the deal, they stop needing to improve it, because nothing is riding on your answer. That is not a flaw in you. It is simply information you handed over earlier than you had to.

Before the next ask, whether it is hours at work or a group project split, decide one thing you would genuinely turn down, and keep it to yourself. Being glad about the opportunity is fine. Announcing you would accept anything is the part that costs you.