If at all is often used to make negatives stronger. It indicates that something is unlikely to happen, or rarely happens, and that it will occur in a negative or restricted way if it does happen. The use of if at all emphasizes notions of scarcity, restriction, smallness, etc.
It never rains for a very long time, if at all. When it rains, it is only for a short time; usually, it doesn't even rain.
He might come late, if he comes at all. We're not really expecting him to come. If he does come, it will be late.
The police usually come late, if at all. The police often come late, however usually they don't even come.
If at all can also be used in questions, most often with question words like 'when' or 'how'. In this sense, it implies two questions together, one more general and one more specific:
When, if at all, will the war end? Will the war ever end? If the war does end, when will that be?
How will a new logo increase our profits, if at all? Will a new logo increase our profits? If it will, then how will it do that?