She started her business 'on a small/tight/shoestring budget' [=she did not have much money when she started her business] and could not afford to overspend.
The government may have to raise taxes to 'balance the budget'. [=to have enough money to provide the amount that is being spent]
The project was completed on schedule and 'under budget'. [=it was completed for less money than had been planned]
(..) Why don't you take off tomorrow? You know, and you could stay home and watch him? Oh, no. No, I can't stay home tomorrow, I have a budget meeting tomorrow. Well, honey, I can't take off, I'm one... one bad pitch away From getting fired... one. Well, I tell you what, I have an idea then. (..)2003 Elf