If you are asking why amino acids contain more 14N than 15N, it is simply because 14N is by far the most abundant isotope in nature, comprising 99.6% of all stable nitrogen found. 15N only comprises 0.4%, so the relative abundance of each in amino acids is simply a reflection of how much is found in nature in general. If you want to know why 14N is the most abundant in nature, then I'm afraid you'll have to ask a nuclear physicist, or read the Wikipedia article on nitrogen isotopes.
Not all amino acids are equal however in terms of 15N abundance. This is related to metabolism in the mammalian host and/or 15N abundance in dietary amino acids. Deamination and transamination in the body determine the 14N/15N isotope fraction and as a result of this metabolically related amino acids will show the highest 15N abundance. However, dietary intake is also important. E.g. in cultures with high intake of animal-based food, N isotopic composition of amino acids will reflect the pattern in the meats and other animal products they eat.
I agree with Thomas Dorlo. Not all amino acids are equal to 15N abundance.N isotopic composition of amino acids will reflect the pattern in the meats and other animal products they eat.
As Greg Cote has already pointed out, the underlying reason for the difference in 14N v. 15N composition in AAs (and proteins) is their typical abundance difference in nature; 14N: 99.63 atom%; 15N: 0.37 atom%. Please, note these are globally averaged "macroscopic" figures. As Thomas Dorlo and Issam Moussa have mentioned, this picture changes the moment you consider "microcosms" such oligopeptides or proteins. Bulk 15N composition of proteins is influenced by the ratio of non-essential to essential AAs and by an organism's position in a given food web. As one moves up in a food web from e.g. primary consumer to secondary consumer (preying/feeding on the primary consumer), bulk 15N abundance in proteins of the secondary consumer will be higher than that observed in the primary consumer. This is called trophic level (isotope) shift. This shift can even be observed in a human if this person slips into a catabolic state (due to either a sever infection or due to crash dieting). In this state a person's body will feed on itself by breaking down muscle to satisfy it AA requirments. As a result proteins such as hair keratin will show a 15N trophic level shift. Separate yet somewhat related to the above is the issue of compound specific difference in 15N abundance between individual AAs which are driven by e.g. differences in transamination (which is reversible) or fractional synthesis rate. Some more detail can be found in chapter I.5.4 if my book. http://eu.wiley.com/WileyCDA/WileyTitle/productCd-1119080207.html