Yes, there are studies where monosodium glutamate (MSG) is used to induce obesity in rodents, but using this fact as an anti-MSG argument is very questionable.
Example of papers using rodent models of MSG-induced obesity
The induction of obesity in rodents by means of monosodium glutamate. - Bunyan et al., Br J Nutr. 1976
The monosodium glutamate (MSG) obese rat as a model for the study of exercise in obesity. - Gobatto et al., Res Commun Mol Pathol Pharmacol., 2002
Of course this is rodent data and as much as animal research is absolutely indispensable to understand human physiology and pathology, it is necessary to critically interpret its results.
Newborn mice were injected subcutaneously with 3 mg MSG/g body-weight at 1, 2, 3, 6, 7, and 8 d of age
and, in the second study
Obesity was induced by MSG administration (4 mg/g, each other day, from birth to 14 days old)
Which is definitely not the same as an adult human eating MSG.
So, how much MSG is consumed by an average person daily?
A 1979 US survey reported 550 mg/die
GRAS Committee on GRAS List Survey. Estimating distributions of daily intake of monosodium glutamate (MSG). Washington, DC: Food and Nutrition Board, Division of Biological Sciences, Assembly of Life Sciences, 1979
(sorry, could not really find a link for this, but it is cited in many other publications...)
A 1991 UK survey reported 580 mg/die
A survey of the monosodium glutamate content of foods and an estimation of the dietary intake of monosodium glutamate. - Rhodes et al., Food Addit Contam., 1991
Another source reports 5 to 12 g/die in European countries
Consensus meeting: monosodium glutamate - an update. - Eur J Clin Nutr., 2007
Taking the larger 12 g/die figure, for a 70kg person that comes to approximately 0.17 mg/g body weight, that is about 17 times less than what was used in the article.
The 550 mg/die figure would give 0.007 mg/g body weight, which is 380 times lower.
That said, I could find one study linking consumption of MSG with obesity in the Chinese population
Consumption of monosodium glutamate in relation to incidence of overweight in Chinese adults: China Health and Nutrition Survey (CHNS) - He et al., Am J Clin Nutr., 2011
although the results have been criticized:
A lack of epidemiologic evidence to link consumption of monosodium L-glutamate and obesity in China. - Bursey et al. - Am J Clin Nutr., 2011
So, in summary altough there are studies showing that injection of MSG in neonatal rodents cause adult obesity:
this is definitely not the most common model of obesity used in a laboratory setting
the fact that MSG had to be injected rather than given orally to get the effect may indicate that the obesity is rather a consequence of the stress due to the injection. Exposure to high level of glucocorticoids (the "stress hormones") during the perinatal period (pregnancy and lactation) has been linked to adult cardiovascular diseases and obesity in both rodents and human.