It has been well documented that weight loss, in particular, rapid weight loss increases your chances of developing new gallstones. In more then one study, it has been shown that new gallstones have formed in as little as only 4 weeks into a VLCD (< 800 cal) . One study claims 25-35% of people who experience rapid weight loss form gallstones after their VLCD diet  and another claims a higher percentage of 54.5% of subjects developing gallstones , not very good odds!
One explanation given for this is that; during rapid weight loss, cholesterol concentrations in the bladder increase - keep in mind this is said to have nothing to do with dietary cholesterol. To add to this, when you eat very low fat and/or skip meals, you do not stimulate your gall bladder to empty itself as often, which worsens the situation, allowing gallstones to form . In fact, one study found a doubling of incidence of hospitalization for gallstones amongst women who fasted overnight for more than 14 hours, compared with women who fasted for 8 or fewer hours .
Gallstones are not just associated with VLC diets. A study was done to see if this also happens on a LCD (low calorie diet). Calories were approximately 925 calories a day spread across 4 liquid meals and one solid meal. By 17 weeks into the study, Six of the 47 patients (12.8%) displayed gallstones with 5 being asymptomatic (no symptoms). The sixth however, had severe pain and required a cholecystectomy at 30 weeks from the beginning of the study. .
Another study showed an increase risk of symptomatic gallstones with weight cycling, weight cycling is where people intentionally lose weight through diet but then later regain some or all of it back, rinse and repeat, this is otherwise known as yo-yo dieting. They found that weight cycling of more than 10 lb of weight loss and regain led to a 31% to 68% increase in the risk for cholecystectomy .
Obesity itself is a pretty big risk factor for gallstones  with many already having silent gallstones (unsymptomatic), in which symptoms may be triggered when doing a VLCD . Other risk factors are diabetes, metabolic syndrome, some medications including oral contraceptives or postmenopausal hormone replacement therapy (estrogen)  as well as females having a higher risk for gall stones which is thought to be due to estrogen increasing cholesterol concentrations in the gall bladder 
I was just reading a book called Gallbladder and Biliary Tract Diseases by Nezam H. Afdhal in Google book search . On page 370 under the heading Lowering of the rate of weight reduction, it said this:
"Several Prospective studies have examined the relationship between weight loss and gallstone formation in the placebo arm of randomized controlled trials designed to prevent gallstone formation during rapid weight loss. In the study by Yang et al, patients who lost more then 25% of their baseline bodyweight during a 16 week very low calorie rapid weight loss diet had an incidence of new gallstone formation more then twice that observed for patients with a lower rate of weight loss. In two other studies, the rate of new gallstone formation increased stepwise with the rate of weight loss. Gallstones developed in only 8% of patients who lost less then 10 lb per month. This increased to 31% in patients who lost 10 to 15 lb per month and 49% in patients who lost 15-20 lb per month. The relationship between rate of weight loss and gallstone formation appeared to be stronger in women then men. These data suggests that the risk of weight loss is limited to only 1 to 2 lb per week."
One study that I was reading suggested a minimum of 10g of fat with every meal to reduce risks  (Keep in mind when I mention that minimum, it is in the context of trying to prevent gallstones only, personally I do believe we need more fat then that for other nutritional reasons). I have also read another study that claims physical activity helps in the prevention of gallstones  and another stating that 34% of cases of symptomatic gallstone disease in men could be prevented by increasing exercise to 30 minutes of endurance-type training five times per week .
Now if you think "well this won't happen to me" think again. There are a low carb, low fat diets in Australia that are very popular. Over here, diets like Atkins aren't very popular at all ever since the Atkins craze slowed down a few years ago. But then you have various low carb, low fat diets which are advertised very heavily on TV and in magazines and readily available. These diets may not always be at very low calorie levels but they can still fall into the VLCD category by the person following it, thinking that less is always more, and this happens a lot!
As you can see, the odds are not great, seriously it seems pretty essential that you participate in regular exercise, make sure to eat enough fat regularly to encourage gall bladder emptying and avoid rapid weight loss unless medically necessary and under medical supervision.
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- Weinsier et al, Relationship between rate of weight loss and gallstone formation, Am J Med 1995, 98.115
- Festi D, Gallbladder motility and gallstone formation in obese patients following very low calorie diets. Use it (fat) to lose it (well). Int J Obes Relat Metab Disord. 1998 Jun;22(6):592-600.
- Dieting and Gallstones, National institute of diabetes and digestive and kidney diseases (NIDDK)
- Sichieri et al, A prospective study of hospitalization with gallstone disease among women: role of dietary factors, fasting period, and dieting. Am J Public Health. 1991 Jul;81(7):880-4.
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- Cirillo et al, Effect of Estrogen Therapy on Gallbladder Disease. JAMA. 2005 Jan 19;293(3):330-9.
- Article: Gallstones and gallbladder disease, University of Maryland Medical Center
- Nezam H. Afdhal, Gallbladder and Biliary Tract Diseases. Google Book Search.
- Gebhard et al, The role of gallbladder emptying in gallstone formation during diet-induced rapid weight loss. Hepatology. 1996 Sep;24(3):544-8.
- Storti et al, Physical activity and decreased risk of clinical gallstone disease among post-menopausal women. Prev Med. 2005 Sep-Oct;41(3-4):772-7.
- Leitzmann et al, The Relation of Physical Activity to Risk for Symptomatic Gallstone Disease in Men. Ann Intern Med. 1998 Mar 15;128(6):417-25.