As I said in the previous related post, the first step in dealing with negative thoughts is 
simply to notice thoughts in general, as mental events that arise and pass away, almost continually. We saw that we can develop the capacity to be aware of what is happening in our lives, by doing the simple exercise of awareness of the breath entering and leaving the body. However, what we quickly notice is often we are too busy thinking about what is happening, preferring that as a way of relating to life.
Still, let us persevere. The more we strengthen this, wider-than-thinking, capacity for awareness, the more we come to understand that thoughts, assumptions and beliefs are mental events and processes rather than reflections of objective truth. In other words,we begin to see the thoughts as passing through the mind, almost like clouds passing accross a clear blue sky. We begin to realize that thoughts are not as solid as we may think they are. We see them simply as thoughts, not necessarily true reflections of reality, and we do not need to follow them. Nor do we identify with them, but rather we try to create a space around the thought and stay there, observing it in silence and without analyzing it, judging it or interfering in any way.
To do this, we can try a second simple practice. We sit and become aware of our breathing. Then we imagine our mind to be the clear blue sky, spacious and bright. As thoughts come, which they inevitably will, we imagine them as clouds passing through the sky. Some are heavy, some are light, but we identify with the sky, not with the clouds. This is the second step in working with negative thoughts, simply noticing that thoughts arise, touching them lightly as if they are clouds, and letting them go.
We are accustomed to identifying with every large or small thought that comes along. But you can train in identifying as the sky instead. When you do, tremendous confidence arises. You see beyond doubt that you can accommodate it all —sunshine, storms, mist, fog, hail —and never give up.
Susan Piver
Mindfulbalance 
What if the clouds are filling my whole sky with heaviness and rain?
Dear Cloud, I apologize for my delay in getting back to you. There are a number of ways in which I can understand your question, so I will reply as best I can to the different possibilities and hopefully you may find it helpful.
What I am proposing in these series of posts is a gradual process by which we work with our thoughts. It is something which requires patient practice. Gradually it allows a greater stability to appear and our capacity to deal with negative thoughts increases. However, this may not be apparent at the start of trying this approach.
Indeed, at the start, what we may find is that we notice how chaotic and continuous our thoughts are. And this may be disconcerting. We find that there are very few gaps between our almost constant thinking, constant planning or worrying . We may even think that the practice is making our situation worse, that our thoughts are racing even more than they were before we sat down. So this alone you may find heavy and alarming because as you say, the thoughts seem to fill the whole mind and the supposed calm underneath is hard to find.
So what we are proposing is a gradual process. By continually coming back to the breath we stop feeding our mental habits. This leads to gaps opening up in our constant thinking. And gradually those gaps can give rise to a greater sense of calm.
However, your word “heaviness” can also refer to not just the quantity of thoughts but also to their content. And it is not easy to work with difficut emotions, such as anger or loss, at the beginning of a process like this. If you find the thoughts are too difficult to sit with in the manner I describe, a number of possibilities can be recommended. With very deep sadness or responding to deep loss, it is recommended that one uses a number of different processes, including talking to trained professionals such as therapists and doctors. At the start of a process such as I am describing here we may not be strong enough just to sit with very strong emtions, such as we may experience in the midst of a personal crisis. Thus the clouds may be too heavy and produce too much rain. If this is your case, I would recommend that you use a number of strategies, including physical exercise, talking to professionals, talking to friends and family, deep breathing as a calming exercise, and other forms of meditation, such as walking meditation, which may be easier.