The tangent elastic forces that act in a small elastic surface has a stronger component in the balloon center direction when it has less air in comparison with the practically full. Therefore, it is more difficult to fill a balloon in the beginning than to continue to fill it when it is already expanded. As you could notice, the balloon of smaller size (David) has a smaller curvature than the other balloon (Goliath). Thus, in the smallest balloon surface (David), a higher resultant force exists in direction to the center (air with more pressure). Due to the fact that the air always moves from high to the low pressures, the small balloon (David) fills the big balloon (Goliath). As can you see, science is in agreement with the mythology, in other words, the small balloon (David) had more strength than the big balloon (Goliath). Don't forget to try! And win bets with your friends!