The Shape of the Line of fate:

As with other lines, the shape and depth of the fate line is important. The heavier the line, the more independent and responsible the owner of the hand is — and the more resistant to change. A very heavy fate line can mean that the owner is stuck in too predictable a pattern.
It can also be an indication that this person pays too much attention to career goals while emotional, health, and intellectual interests are given short shrift. However, success in life is as dependent on these things as it is on hard work. Overall, though, a strong fate line is a positive thing, indicating that you are self-motivated, trustworthy, and strong. A deep line shows an ability to concentrate and an interest in the work itself.
A weak fate line shows a lack of direction and control, putting you at risk. A thin line of destiny shows a lack of commitment and stamina. And an irregular or fragmented line of destiny shows purposelessness, changeability, ill temper, and a person who is not in charge of one's own life.