We establish improved uniform error bounds for the time-splitting methods for the long-time dynamics of the nonlinear Schr\"odinger equation (NLSE) with weak nonlinearity. By a new technique of regularity compensation oscillation (RCO) in which the high frequency modes are controlled by regularity and the low frequency modes are analyzed by phase cancellation, an improved uniform error bound is established. Numerical results are reported to validate our error estimates and to demonstrate that they are sharp.