If you’ve found your relative’s name on a petition, remember that petitions were not all signed on one day. Like modern petitions they were circulated and signatures were not all collected in one afternoon, one day, or even within one week (usually).
Petitions may have been taken around the neighborhood (village, town, township, county, etc.) and signed over time. The petition may have been kept at the local tavern or other common gathering place where signatures were obtained. Signatures that “look a lot alike” may have been all made by one person for themselves and others who agreed the petition at the same time, but could not sign themselves.