Emirates International Flight and carry-on baggage. Can I take a laptop backpack in addition to the one carry-on bag?

It quite often depends on the airline. From tomorrow, for example, Jetstar is going to be strictly limiting carry-on to 7kg (~15.5lbs). AirNZ sometimes does, sometimes doesn't. Emirates may well only weigh if your bag looks heavy, big, or if they have time.

Basically, yes, you'll need to put more in your checked luggage. Your carry-on is supposed to be just what you need for the flight. Do you really need your phone, camera etc. on the flight? 15lb of stuff?

(I'm not judging you, mine has been over 25lb in the past, and a friend and I once split an entire stereo system between our carry-on bags. I'm merely trying to encourage you to decide if you really need it, and explain why the airlines feel you don't need more than 15lb of stuff for a flight. Light jacket, medications, book or laptop/tablet is usually enough for most people.)

Some people, especially with airlines often charging for checked luggage, now try to take everything in their carry-on, so it's increasingly likely that the airline will weigh your bag.

A quick google search indicates others have had their carry-on weighed, so there's no reason to expect yours not to be.

EDIT: after you changed the question to be specifically about taking a laptop bag and a backpack, it depends on which class you're in for the flight.

As per the Emirates website FAQ:

Economy Class passengers are permitted one (1) piece of carry-on baggage, either a handbag or laptop bag, subject to the following size and weight limitation (7kg)

So no, you can't take two bags including your laptop bag, unless you're in business or first, where it's:

First Class and Business Class passengers are permitted two (2) pieces of carry-on baggage: one (1) briefcase plus either one (1) handbag or one (1) garment bag, all subject to the following size and weight limitations