Consider the scenario of a gardener cutting grass with a lawnmower.
Would he experience more friction when pushing the lawnmower or pulling it?
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Because of the way humans tend to push and pull, when they push something, they tend to push it closer to the ground in some sense.
Now because friction is understood as the interaction of the two surfaces, there is more scope for such interaction when the roller is pressed onto the ground instead of pulling it away.
Quantitatively, like Rakshit said, F f r i c t i o n ∝ N . And when the effective weight is increased, the Normal reaction increases, so as to balance it.