For a discussion of the factors that effect helix formation in gelatin-based gels, I recommend "All Gelatin Networks" by Christine Joly-Duhamal et al., in Langmuir, 2002, 7208-7217. This paper provides a nice overview in the context of a recent study that was trying to elucidate the structure-property relationships in these systems.
The explanation for why high-molecular weight gelatin tends to have a greater percentage of triple helices can be traced back to the Zimm-Bragg model of coil-helix transitions (J. Chem. Phys., 1959, 31, 526-35). Briefly, this statistical mechanical model describes the tendency of a polymer chain to undergo a helix-coil transition using two parameters: (a) the equilibrium constant that determines whether an existing helix will propagate and (b) the likelihood of a new helix being initiated. Since helix propagation is much more favorable than helix initiation, long chains (that tend to have some helix content) will have higher percentages of helical structure.
I am less sure about the second aspect of the question: i.e. why gelatin also stabilizes foams, but I can make an educated guess. Foams are examples of aerogels: in other words a physical network that is "swelled" by a gas such as air. Gelatin usually is encountered in the context of hydrogels, i.e. a physical network that is swelled by a liquid, such as water. The two phenomena are closely related, and many materials that form networks will form both hydrogels and aerogels. For a more in depth discussion of gels, check out any introductory polymer textbook.
Gelatin is a protein and proteins stabilize foam better than ordinary surfactants such as a foam created by soap or detergent. Once a foam has been formed, there are three processes which affect its long-term stability near equilibrium.
Drainage: the draining of liquid from foam.
Disproportionation: the change in foam bubble size distribution caused by gas diffusion from small to large bubbles.
Coalescence: the fusion of foam bubbles.
A surfactant foam drains faster than a protein foam. This difference is also related to the possibility of the protein forming a stagnant surface layer. Furthermore, proteins are irreversibly adsorbed at the interface, whereas surfactants are not. Therefore, proteins slow down the disproportionation process more than surfactants can.