Will a horizontal 2x4 support my body weight?
I expected to see a double 2x4 header while you have a single; I'd make it a double.  FYI, you can look up weight it can support on beam span table/calculator.  You can rely upon the jack studs to support the weight but I'd add metal brackets (e.g. Simpson Strong Tie) to add additional support (i.e. for the not strictly vertical forces) since you're jerking around and brackets are less than $1 each.  Bracket the king studs to the header and two more brackets for the cross-beam.
P.S. Your stamp means it's kiln-dried southern pine/fir