Using heavier weights is one of the keys to building muscle and getting stronger. Go too heavy too soon, however, and you'll undoubtedly use poor form and put yourself at risk of injury. How quickly you progress from one set of dumbbells to the next depends on the type of exercise you're doing, your currently training level and a number of different factors.
In the Beginning
When you start out lifting weights, your body adapts relatively quickly and progress can be fairly rapid. The University of Rochester Medical Center advises starting with weights that feel light. You should be able to do at least 15 perfect repetitions without too much trouble for a weight to be classed as light. Adopting this method means that jumping up to the next level shouldn't be too much of a challenge, and you may only need to use one pair of dumbbells for one or two workouts before going heavier. Move up in small increments of no more than 5 pounds each workout and keep an eye on your form -- using poor form is a sure sign you've gone too heavy, too soon.
The longer you've trained and the more experienced you become, the harder you'll find it to increase your dumbbell weights. Most intermediate trainees will follow a linear microcycle, which could be three sets of 12 reps for four weeks, three sets of 10 with a slightly heavier weight in weeks five to eight and four sets of eight with a heavier weight again in weeks nine to 12. You would then go back to week one, but use a heavier weight that first time round. This means you'll be increasing your dumbbell strength every 12 weeks.
The Stability Factor
Unlike weight machines, your stabilizing muscles have a lot of work to do when lifting dumbbells. On dumbbell exercises, the stabilizing muscles often become fatigued before the main muscles, writes sports scientist Jim Stoppani in "The Encyclopaedia of Muscle & Strength." This means it's often harder to increase the weights you're lifting on a dumbbell chest press, for example, than on a machine chest press or even a barbell press. If you find that when using dumbbells, you're having to put more effort into balancing the weight and the target muscles aren't being suitably worked, drop down a weight and build up the stabilizing muscles before going heavier. The type of exercise matters too. You'll get stronger faster on a multi-joint move -- like dumbbell rows or overhead presses -- than you will on a single-joint one like curls or overhead extensions.
Making the Effort
How quickly you gain strength and work your way up the dumbbell rack is also dependent on the effort you put in. If you push yourself and train close to muscular failure, you should be able to progress fairly rapidly. Focus on performing good quality reps, work your whole body evenly and move up to the next weight when you feel like the dumbbells you're using aren't providing enough of a challenge. For a weight to be challenging, it should cause you to reach muscular failure on the last rep. If you're performing a set of 10 for instance, reps one to five should feel okay, reps six and seven should be tough and reps eight to nine should be immensely challenging. At rep 10 your form will probably start to break down, which is a good indicator that you're lifting heavy enough and shouldn't try to push out any more reps.