Good weather [with-で] picnic [of-の] fun [subject-が] increased.
増す ('to increase, grow, add to') is an intransitive verb used here with 楽しさ ('fun-ness'). The で marks the cause/means — 'with the good weather.' 楽しさ is the noun form of 楽しい, using the ~さ suffix that makes adjectives into abstract nouns.