Is it true that an overweight child will eventually have a harder time getting and staying in shape as an adult?

Yes. If you think about it, the major problem with obesity is to change your eating and exercising habit (although there are other reason for it as well). As hard as it may sound, the easier time to change those habits is when they are young. As human beings, the older we get, the harder to change those habits. So if we can't change those habit when our kids are young... It is even more difficult later.
Yes. Obesity (overt heavy weight, body mass index over 95th percentile) at any point in childhood including infancy, puts affected children at higher risk to become obese or overweight adults.