Lifting heavy isn't enough
The idea that lifting heavy weights by itself causes bulk is a myth. Understanding why is more complicated. First, let's address the specific claim at issue, that women need to stick to 5-pound weights. Kathleen Ekdahl points out that five pounds is too light to even count as weights!
In order to avoid this gain in muscle mass, women are told to lift very light weights. This recommendation is oftentimes interpreted to the extreme, and women perform many repetitions with 3 or 5 pound weights. Unfortunately, without sufficient load (weight), the muscle will not change, and the goal of "tone" and "shape" cannot be achieved. A change in the shape or tone of a muscle is created in the same way that size is created, with hard work and consistency!! In order to shape or tone your muscle, you must lift a weight that is heavy enough to create muscle fatigue (also known as failure). Working your muscles to fatigue means that your muscles refuse to lift/move the weight in a correct and safe fashion. Working your muscles to fatigue will not necessarily create large, unsightly muscle mass. Even if you work your muscles to extreme fatigue, rest assured, that the majority of women are genetically unable to create large muscles because they lack sufficient hormones or body structure to do so.
It's really hard to get huge muscles and look like a professional bodybuilder. If it were easy, more guys at the gym would be sporting forty-inch biceps. Unless you're trying specifically to get bigger and bulkier, it's unlikely that it'll happen by accident. More likely, lifting heavy weights will burn fat and build size-appropriate muscle. These young women lifting heavy weights don't seem concerned about supposed problems with bulkiness, right?
In Practical Programming, Mark Rippetoe and Lon Kilgore sum up the issue well, next to a photo of one of their young female trainees:
Women are more likely to believe that weight training is unimportant to health and sports performance than men. There is also a social and media-driven misconception that all weight training produces big, masculine, muscle-bound physiques. This generally does not occur in women without anabolic steroids.
Women are generally steered towards low-weight, high-repetition "toning" exercise routines. The New York Times reviewed the science and came to the conclusion that "for better tone, try fewer reps and more challenging weights."
Rippetoe and Kilgore explain the fact that the low-weight, high-rep exercise routines typically marketed to women are just ineffective hypertrophy programs. In other words, they're designed to make bigger muscles (which is the opposite of what these women want), and they don't even a good job of it:
The modern fitness industry's concept of "toning" muscles is specious--it might sound cool, but it lacks any tangible and definable meaning. The term "muscle tone," or tonus, describes an electrophysiological phenomenon, a measure of ionic flow across muscle cell membranes.... Lack of exercise leads to poor tone, aerobic exercise improves tone a little bit, low-intensity weight training improves tone more, and high-intensity training improves tone the fastest.... Most exercise programs that claim to improve muscle tone are actually lower-intensity hypertrophy programs and are only moderately effective for improving muscle tone. If "tone" is the goal, strength is the method.
Many women have discovered that strength training is the path to what they consider to be "tone". Heavy strength training can allow someone to stay the same weight while dramatically changing their body composition from fat to muscle.
More important factors
Whether the barbell is loaded heavy is almost irrelevant compared to diet and volume. Eating big and high-weight, high-volume programs will get you bigger in a hurry. Eating a caloric deficit, or at caloric maintenance, plus a low-volume high-weight program, will get you a great deal stronger but not add mass. Triples at 90% of 1RM with normal caloric intake is dramatically different for mass and body composition from 5 sets of 5 at 80% of 1RM with a hefty caloric surplus and a gallon of milk a day.
Tim Kontos, David Adamson, and Sarah Walls at EliteFTS address the importance of volume, as part of a broader attempt to dispel the myths that keep women away from lifting weights:
Muscle bulk comes from a high volume of work. The repetition range that most women would prefer to do (8–20 reps) promotes hypertrophy (muscle growth). For example, a bodybuilding program will have three exercises per body part. For the chest, they will do flat bench for three sets of 12, incline for three sets of 12, and decline bench for three sets of 12. This adds up to 108 total repetitions. A program geared towards strength will have one exercise for the chest—flat bench for six sets of three with progressively heavier weight. This equals 18 total repetitions. High volume (108 reps) causes considerable muscle damage, which in turn, results in hypertrophy. The considerably lower volume (18 reps) will build more strength and cause minimal bulking.
Heavy weights will promote strength not size. This has been proven time and time again. When lifting weights over 85 percent, the primary stress imposed upon the body is placed on the nervous system, not on the muscles. Therefore, strength will improve by a neurological effect while not increasing the size of the muscles.
Reddit's /r/fitness subreddit is pretty dedicated to showing before-and-after examples of women who engage in heavy-lifting strength programs. Here's one. Sometimes those anecdotes are of the form "it worked for me", but occasionally women are unhappy with their results. Sometimes that's because heavy lifting didn't work, but just as often it's that the program worked as expected, but the woman simply considered the results to be negative.
JCD Fitness has some longer takes on the issue that make great use of women's personal stories. One of the points brought up there, as well as on reddit, is that marketing messages have effectively brought body image issues into the problem. At bottom, everyone has a different definition of "bulky", and sometimes women really do want to look like an undernourished model at her peak of starvation and airbrushing. In those cases, radical weight-loss programs really would be the best path to achieve those (possibly problematic) goals, and lifting weights and otherwise doing impressive things might not be the right approach.