Those are some tough requirements. For actual vacuum cleaners, there are none that fit that description, you can have one or two of your requirements, but you won’t find all three. The exception to this would be something in the form of a stick vac such as the Electrolux ErgoRapido. A stick vac is a handheld vacuum that is attached to a handle and usually has a carpet/bare floor head. They are adequate for quick pick-ups, but not for any serious cleaning.
If you can come up on your price a bit you can get an Oreck Signature, XL Pro, or Element. Oreck uprights weigh in at about 8 pounds, but they are usually $200 and up, depending on the model you choose. The Hoover UH30010 is very similar to the Oreck XL series and slightly less expensive. These vacuums do combine lightweight with performance.
You may also be interested in the Shark Navigator or the Shark Navigator Lift Away. These are light and powerful vacuums contained within a small package. They are all under 15 pounds and very nimble.
Another way to go would be a canister vacuum. With a canister, you are only operating a hose and wand, you’re not hefting around the entire vacuum. Canisters such as the Oreck Little Hero, Quest, or Quest Pro are very capable machines. Nearly all vacuum manufacturers have canister models to choose from, however, as earlier stated, you’re not going to find a really good one for under $100.