It may not be easy to convince a child for walking on his own. But you may relieve yourself of the load of carrying a child constantly by:

Offering to hold the hand of the child.

Setting limits, like you'll carry the child for five minutes, but then he will walk for ten minutes on his own, or you will carry the child to the store but the child will have to walk inside it.

If you're at home and the child just wants to be held to see what you're doing, you may make him sit on a high chair while you cook, so that he can watch you while he can be busy trying to pull the lid of a container, or doing something else to keep his hands busy.

While walking, if the child feels that he's not able to see what you're seeing and thus, wants to be carried, you may try showing him interesting things at his level, such as flowers, dogs and other children.