I'm not sure what you are referring to by "weathering mothers". I am familiar with some of the telomere research because of my work with Aplastic Anemia & MDS.
Have you looked at this review: Aubert, G., Hills, M., & Lansdorp, P. M. (2012). Telomere Length Measurement - caveats and a critical assessment of the available technologies and tools. Mutation Research, 730(1-2), 59–67. doi:10.1016/j.mrfmmm.2011.04.003
They cover the basics of telomere assessment and present the pros & cons. There are some interesting research publications that have cited this article in Pubmed. It might be a good starting point.
I use 'weathering' as a construct coined by Arline Geronimus that stems from her work studying racial/ ethnic perinatal health disparities in preterm birth rates among African American women.
Southern blot is the most common method to look at telomere length, which we have used extensively. However, it depends on how sensitive you need it to be. It may not be sensitive enough to detect very small differences in length over multiple samples. Some PCR based methods are more involved, but may give you more sensitivity after optimization.