We show that de Rham cohomology sheaves of a smooth non-Archimedean space have a functorial decomposition through local weights. In particular, this answers a question raised by Berkovich for 1-forms. We also reveal a connection between de Rham cohomology sheaves and the (bi)complex of sheaves of real forms defined by Chambert-Loir and Ducros via tropical charts. As an application, we show that integrations of closed real forms on an algebraic cycle vanish if the cycle is cohomologically trivial (in algebraic de Rham cohomology). Speaker(s): Yifeng Liu (Northwestern University)