How does density of alkali metals increase down the group?
$Density=mass/volume$

1) If mass is increasing and volume is decreasing, then density (mass/volume) will increase.

2)If mass is decreasing and volume is increasing simultaneously, then the density (mass/volume) will decrease.

*3)If both mass and volume are increasing, then we need to check which one of them is increasing at a faster rate(since both are contradictory factors)

a) If mass is increasing at a faster rate than volume, then density will increase.

b) If volume is increasing at a faster rate than mass (i.e denominator in mass/volume is increasing making the overall fraction smaller), then density decreases.

You can apply same logic when both volume and mass are decreasing simultaneously.

Generally, we see that in alkali metals the rate of increase of mass is greater than rate of increase of volume, therefore the density increases down the group.

Also, note that there is no definite reason for why mass is increasing at a faster rate than volume. So asking "why" does it happen isn't a great question.