All I can say AOG is that in the case of my immediate locality, and that of most of working class South Wales, there appears to be no link between obesity and the ethnicity of the local population, unless the link is between white people and obesity.
In fact, if we were to have no Asian food outlets at all, the non-white minority would be even smaller than it is at present ! Most of then appear to be involved with the provision of our national dishes, like Chicken Jalfrezi and Duck with Ginger and Pineapple !
By the way, quite a large amount of the old-fashioned chip shops are owned by second and third generation Italian families. That goes for bakers and ice cream makers too. That started about a century ago, when Italians came to South Wales to work in the mines, and it increased after WW2 by inmates from an Italian POW camp not going home after VE Day.
Mind you there is a popular saying that goes " Wales is Italy in the Rain" after our love of singing and Opera, as well as our sunny disposition !