Normally overlapping peaks results by template DNA or sequencing primer. Here are some potential reasons:
1) Sequencing primer has alternative complementary site on the template DNA.
2) Template DNA is impure. If the template DNA is a plasmid or E. coli culture, the clone might be contaminated. If the template DNA is PCR product, it might contains some unrelated DNA but with similar size with the template.
3) Presence of unique structures on the template DNA, such as poly A or poly G, hairpin structure, etc.
4) Primer degradation, impure primer, or primer with poor binding specificity.