I found the following rule in your custom CSS, which looks like a duplicate of the same rule that comes in the theme stylesheet already:
.widget {
clear: both;
margin: 0 0 2.2em;
}
That is making a 2.2em margin space at the bottom of all widgets. You could adjust that number and it would affect all of the widgets. Or, you could add a more specific rule to adjust the bottom margin just for image widgets like this:
.widget_image {
margin-bottom: 0;
}
I also found this rule in your custom CSS:
.wp-caption {
background:#fff;
margin-bottom:1.625em;
max-width:96%;
padding:9px;
}
The margin on that rule affects the images with captions in the post content as well as the sidebar, if you wanted to adjust the spacing just for captions in the sidebar and remove the bottom spacing from the rule above, you would add this:
widget_image .wp-caption {
margin-bottom: 0;
}
So, to remove ALL the extra spacing from the other rules you've already applied and just remove extra spacing from image widgets with captions int he sidebar, add the following:
.widget_image {
margin-bottom: 0;
}
.widget_image .wp-caption {
margin-bottom: 0;
}
Note that if this removes too much space, you can just add in some numbers other than zero.