As I said, it really depends on what processor you need. It sounds like the weight is a higher priority than the bigger quad-core CPU, and given that:

If you can stretch the budget a little, and you don't see a need to have an upgradeable system, the system I'd encourage you to look at first is the Lenovo X1 Carbon (current is 4th generation with i5-6xxxU processors). At 2.6lbs, I'm fairly sure it's still far and away the thinnest and lightest 14" business ultrabook. You might look and see if there are any refurb or remaining stock 3rd-generation ones with the i5-5xxxU processors.

None of the other ones I'm aware of are quite as light as 3lbs at a 14" screen. If you can stretch the weight limit to 3.25 lbs, the Dell E7470 (or a last-gen E7450) is worth looking at. The T460s (or a last gen T450s) is one step heavier still but still only around 3.5lbs.

The Dell XPS 13 is not a full business notebook, and won't be quite as sturdy as the X1 or the slightly heavier ones above. It's also going to be hard to get the specs you want in your budget: to come in under $1000, you'd need to buy it with a smaller SSD and upgrade yourself. They are nice machines, and incredibly compact.

Any of the 12" business ultrabooks will meet your needs if configured correctly: X260 and E7270 from this generation or the X250/E7250 from the last.

Personally, if I was looking for a new machine like yours, I'd be looking at refurbished Dell E7450 or E7470 from their Outlet. There are some E7470s matching your specs for about $1200, which after the current 25% coupon (and there's practically ALWAYS a coupon; they expire for a few days and then come back) you'd be looking at about $900 before tax and shipping, and with free ground shipping that's under $1000 even in high-tax California (if just barely.)

I was going to suggest getting a base model and upgrading the memory and SSD, but it's not actually any cost savings right now.

The deals on the 12" models are not quite as good; would be around $1100 once you need the 500-512GB SSD. If you needed to to meet your price range, you could get one with a 128GB SSD and then upgrade it yourself (about $150 for an aftermarket SSD; I recommend the Crucial MX200 M.2 2280SS for the E7270) which would be just under $1000 combined.

In my experience, quality control is actually BETTER on refurbished business-line Dells than on new stock; an awful lot of the business machines are corporate returns that were never actually used by an end-user. They come with the same warranty as new.