In order to meet the targeted dispersion requirements of applications, hybridized modes of coupled waveguides, whose dispersion characteristics can be significantly altered around their mode cross-point, have been recently investigated. The applications have been applied to microresonators based on concentric waveguides with a thin silicon nitride layer. However, it is still challenging to achieve a low and flattened anomalous dispersion profile just by optimizing the gap width between the waveguides. We propose to investigate the dispersion characteristics of coupled silicon nitride waveguides with a partially etched gap. It is shown that low and broadband anomalous dispersion can be achieved based on relatively thin 515 nm thick silicon nitride layer waveguides. The mechanism of a partially etched gap on dispersion engineering can be attributed to the tuning of the coupling strength between the waveguides. Therefore, when combined with other design parameters, it offers an additional "tuning knob" of advanced dispersion engineering when designing such coupled-waveguide devices for nonlinear photonic applications.