will the heavy jar or the light jar reach the bottom of the ramp first?

I am assuming that you are talking about rolling two jars down a ramp.
Or rather letting them roll under there own steam. I am also assuming
that both jars are equal in shape, size and dimensions and hence the
only difference is their density.
The force acting down the ramp is given by Mg Sin (theta) where M =
Mass, G= Gravity and Theta = angle of the ramp to the horizontal.
Hence more mass = more force down plane therefore would result in more
speed.
Of coure this assumes that the extra mass is evenly distributed and fixed in place.

Please don't forget that acceleration is given by force / mass.

This is a variation of Galileo's experiment with light and heavy balls
(which he rolled down ramps). I'd expect that the heavy one would win
slightly due to the effects of air resistance, but if we ignore air
resistance they should reach the bottom of the ramp at the same time.