Counter example for strong and weak Pareto optimality
There are two goods and two consumers, no production. The aggregate endowment is strictly positive. Consumer 1 cares only about the amount of good 1 they consume, with more being better. Similarly for consumer 2 and good 2. Preferences here are continuous and monotone but not strictly monotone. The allocation in which consumer 1 consumes the entire aggregate endowment is weakly Pareto optimal but not strongly so.