Reg wrote, "Try suspending the measuring instrument in mid-air to
remove your body capacitance and see if it makes any difference to the
measured impedance."

Even better (perhaps), set up the antenna as you plan to use it,
including balun and feedline. Make your measurements at the "other"
(non-antenna) end of the feedline. Back out the effects of that length
of feedline, and you have the antenna feedpoint impedance in that
particular environment. If the line is reasonably long so you and your
measurement device are at least a couple wavelengths from the antenna,
and reasonably well decoupled from the antenna so that there isn't a
lot of "antenna current" on the feedline, your measurements should be
essentially independent of your presence and the presence of the
analyzer.

Cheers,
Tom