I suggest that there is something a bit odd about the rectifier.
Look at the X1 trace, alternate "dips" do not go down to 0v.
Maybe a leaky diode?
Combine the higher impedance of the X10 probe with the leaky diode, and the alternate dips can just float at a higher voltage.
When you put your 1k load, the small leakage of the diode is completely swamped by the current drain of the load.
Also, with the 1k load, I guess that the alternate dip discrepancy disappears.
JimB