Statement I: Pulling a lawn roller is easier than pushing it.
Statement II: Pushing increases the apparent weight and hence the force of friction.
Suppose the roller is pushed as in figure (b). The force F is resolved into two components, horizontal component which helps the roller to move forward, and the vertical component acting downwards adds to the weight. Thus weight is increased. But in the case of pull [fig (a)] the vertical component is opposite to its weight. Thus weight is reduced. So pulling is easier than pushing the lawn roller.