Why do people lose a lot of weight when they first start to exercise? Why does it become harder to lose weight with time?

your  body taps into your fat reserves for extra energy,once those reserves deplete more and harder workouts are needed in order for the body to give away.Those reserves which he tries to maintain at about 10% of your Total body weight are for  health reasons.

The first reason is that the more you practice the more your body adapt to the activity and learn it. With better technique and less effort you get the same performance.that's why it's better to keep track of what you're doing and try to increase the load and intensity. .the second reason is less fat you have the hardest you loose it.

The theory of marginal return is applicable in this activity too,. In weight reduction through exercise excess  fat is burnt .5 kg  reduction on 100 Kg body weight is 5% where as  5% of 95 Kg is  4.75 kgs only. So as the weight is reduced the same level of effort would not give the same initial reduction and is harder to reduce the weight in same pace