A scar might become thicker because of how the body heals. A part of a scar might be thicker if it had a disrupted or abnormal healing process. We need collagen to repair the tissue after injury or surgery. As a wound heals and the scar forms less collagen should be produced, this process might get upset due to prolonged inflammatory state.

Sometimes the body can overproduce collagen. We can get exaggerated production of collagen as a protective mechanism to strengthen the area, this could happen if there is too much stretch tension or not enough support.
If a wound is deeper the body can respond by producing more collagen as it thinks in needs to reinforce the area. The area of the body where the scar is located
Even genetics can play a part in the type of scar, darker skin tones are more prone to thicker scars.
These thicker scars are also known as hypertrophic or keloid scars. Keloid scars can be very itchy towards the outer edges and painful in the centre. Hypertrophic scars tend to be more itchy.
Some of the medication given to relieve pain especially in the early stages can actually induce histamine release which could then lead to the itching which could lead to inflammation and so the process goes on.
Making sure your scar is hydrated can help. Speak to your scar therapist about silicone gel sheets to use as a barrier on keloid scars, they would need to be used longterm to notice a difference in the texture and colour of the scar and to help change the appearance. Keloid scars need specialist help, massage could worsen the scar. A keloid scar will be red, raised it will have spread outside the original scar site. A hypertrophic scar will be raised, but should still be within the original scar site.

Prevention is better. Reduce your risk of a pathological scar developing. Be sensitive to forces placed upon the scar. How much stretch tension, how much shear force there is on the scar. Also being sensitive to swelling. Eat well, move well and have a good self care routine.