Please cite only credible information here. I saw one site that said muscle weighs 3 times more than fat but they don't cite any references so I wouldn't consider that credible. I also saw one site that said fat weighs 7 lbs per gallon; but again, no references about where the info came from.
A. Muscle density is 1.06 g/ml and fat density is (about) 0.9 g/ml. Thus, one liter of muscle would weight 1.06 kg and one liter of fat would weight 0.9 kg. In other words, muscle is about 18% denses than fat. This should not be confused with the "energy density" of muscle and fat, which may be where you got the 3x figure that you mention in your question.
I have made a special effort to find credible sources for the answer. Below I provide sources for the two numbers separately.
1. The density of mammalian skeletal muscle is 1.06 g/ml. "... 1.06 g/cm-3 which is the density of mammalian skeletal muscle".
Source for quote: The Journals of Gerontology Series A: Biological Sciences and Medical Sciences 56:B191-B197 (2001) Specific Force Deficit in Skeletal Muscles of Old Rats Is Partially Explained by the Existence of Denervated Muscle Fibers Melanie G. Urbancheka, Elisa B. Pickenb, Loree K. Kalliainenc and William M. Kuzon, Jr.a,d http://biomed.gerontologyjournals.org/cgi/content/full/56/5/B191#R23 Reference given by the authors: Mendez J, Keys A, 1960. Density and composition of mammalian muscle. Metabolism 9:184-188.
2. The density of adipose tissue (fat) is about 0.9 g/ml "...by multiplying the density of adipose tissue (0.9196 g/ml)"
Source: Association of adiponectin and resistin with adipose tissue compartments, insulin resistance and dyslipidaemia M. S. Farvid1, T. W. K. Ng2, D. C. Chan2, P. H. R. Barrett2 and G. F. Watts2* http://www.blackwell-synergy.com/doi/abs/10.1111/j.1463-1326.2004.00410.x
"...on the assumption that the density of adipose tissue is 0.9g/cm3" Source of quote: Pediatric Research 55:437-441 (2004) Distribution of Adipose Tissue in the Newborn TRACEY A.M. HARRINGTON, ELIZABETH LOUISE THOMAS, GARY FROST, NEENA MODI and JIMMY D. BELL Source given by authors: Ross R, Léger L, Guardo R, De Guise J, Pike BG 1991 Adipose tissue volume measured by magnetic resonance imaging and computerized tomography in rats. J Appl Physiol 70: 21642172
I hope you find this to be useful and a complete answer to your question. Let me know if there is anything I can clarify.