PARIS — Amid signs that Americans are tiring of sending weapons to Ukraine after two years of war, President Joe Biden this week will huddle with other world leaders in search of new ways to get aid to the country as it struggles to fend off Russia’s invasion.

Biden will participate in a three-day meeting in Apulia, Italy, of the Group of Seven, or G7, the organization formed by the world’s largest industrialized nations, where a major topic will be tapping $300 billion worth of frozen…