Certain kinds of cancer in early age are associated with silencing of tumor suppressor genes such as CDKN2A and RASSF1a. There are other examples of tumor suppressor genes that are silenced by hyper-methylation.
Methylation is a very location-specific mechanism for gene repression, such that hyper-methylation of the gene promoter is primarily linked to reduced transcriptional activity.
In the context of adolescent diseases, imprinting disorders such as Angelman and Prader-Willi syndromes are classical examples of abberent imprinting disorders: Article Prader-Willi and Angelman syndromes. Disorders of genomic imprinting
If interested in somatic diseases associated with DNA hypermethylation, the above mention of cancer is a great example. Specifically for adolescents, osteosarcoma and various leukemias (e.g. Acute Myelogenous Leukemia, AML) are malignancies affecting younger adults:
Article An integrative analysis of DNA methylation in osteosarcoma
There are also some evidence that there are some patterns of differential methylation observed in human and nonhuman species with altered maternal care are also characteristic of children who experience early maternal separation.
DNA methylation is a dynamic process that occurs every moment inside the cells of the body from any part. The methylation-demethylation is largely driven by environment. In a nutshell, almost all the foreign or xenobites have the ability to change the epigenetic makeup of the cells. As a person ages, such environmental epigenetic signals accumulate over time, resulting in more and more hypermethylation of genes. Even ageing of the cells produce metabolites responsible for epigenetic alterations. NOTE that it is not only the hypermethylation that is responsible for gene silencing, there are all other dynamic processes like histones modifications and small RNAs such as miRNAs that all work in cascades to silence the genes. This is about the first part of your question.
Now regarding the second part, some people inherit epigenetic markers such as hypermethylated DNA (Some epigenetic changes get inherited although most of them get reset during gametogenesis); i.e the nature which along with nurture causes early onset of certain diseases such as cancers. Even certain autoimmune diseases are related to abnormal epigenetic machinary such as DNA methylation. But in my opinion, it is rare for a person without any disease at birth and later develop a disease specifically within teenage due to hypermethylation of DNA in normal condition because such hypermethylation require some strong stimuli or in born defect in the state of epigenetics. For example, a portion of young patients treated with chemotherapy (stimulus) develop infertility (disease) because of epigenetic changes; Smoking changes the methylation state of the DNA, which may predispose people to cancer; Errors in the genes for histone demethylases help in development of cancer.