We introduce a modeling framework for continuous-time relational data that allows detecting the fine-grained dynamics of network formation and change in financial markets. We propose newly derived Relational Event Models with time-weighting functions and corresponding time-weighted statistics as a suitable approach to capture the temporal aspects of observed network processes (i.e., memory) as well as a variety of extra-dyadic microstructures that include tie frequency (i.e., trading intensity) and tie value (i.e., traded amount). By specifying novel statistics and fine tuning weighting-function parameters, we show how this framework allows (1) obtaining more accurate representation of market dynamics, (2) disentangling competing micromechanisms of network formation and change, and (3) assessing their relevance. Also, by comparing alternative specifications of time effects, we emphasize the parsimony afforded by our approach. We illustrate the merits of our modeling framework in a study of the interbank liquidity market during the 2008 financial crisis.