If you want to trace back to a person with active-duty or patriotic service during the Revolutionary War who is ancestor of you or a loved one, there is no substitute for a step-by-step working back in time to an ancestral Bergheimer (or spelling variant such as Burkheimer, Berchheim) who was born no later than the 1760s and who was in America before 1783.
Trying to work forward from a known Veteran or Patriot can be a wild-goose chase. One of the two top genealogical mistakes is "same surname = same family."
The Penna. State Archives has posted cards listing militiamen and some others that you can search here:http://www.digitalarchives.state.pa.us/
--read the introduction and scroll down to the link to the page where you can connect with Rev. War soldiers' listings.
All able-bodied free white males of age roughly 16-60 (varied by time and place) was required to be available for militia duty for defense within the County. Many rosters exist for those who showed up for regular drill, but this was not "active duty". The vast majority of militiamen did not see active duty, which could include patrolling, guarding prisoners, or escorting supplies bound elsewhere.
The DAR has posted information on persons who were patriot ancestors of past and present members of DAR. You can read the introductory pages and do a search through this page:http://www.digitalarchives.state.pa.us/
There is no "wild card" search capability, so try every spelling variant you know of.
You can search Revolutionary War Continental Troops service records and Congressional Pension application files on footnote.com and view the results, but not download, print or copy the material without subscribing.