Understanding the behaviour of a spectrum analyzer
This is actually said in a comment, but you have noticed in practice that feeding a sinusoidal signal through a bandpass filter generates an output sinewave which grows gradually. The frequency sweep mixing transfers a moving window of the analyzed frequency range to the passband of the I.F. filter. The faster is the sweep (Hz/second) the shorter burst of your signal goes through the I.F. filter and the lower is the built up max. oscillation amplitude at the output of the filter => the lower peak you see.

If you have some spare time you could easily find the phenomena with a circuit simulator (assuming you can construct there a bandpass filter). Feed a sinewave which starts at t=0 to a filter and see, how the output amplitude grows gradually to the final value. The growth rate depends in a complex way on the bandwidth and passband gain vs frequency curve of the filter, but the manual of your analyzer surely tells how many Hz/second the sweep rate can be if you have selected a certain resolution bandwidth and expect the measured amplitudes have a certain maximum error in decibels. Generally the allowed sweep rate decreases if you make the resolution bandwidth smaller or allow less amplitude error.