This paper addresses the problem of fully-connected hybrid analog-digital (HAD) beamforming design for a multi-user and multi-beam ISAC setup. Traditional approaches to this problem involve a two-step process: first, a fully digital precoder is obtained, then the HAD beamforming is resolved by minimizing the Euclidean distance to the previously designed fully digital precoder. However, the main drawback of this method is that the communication or radio-sensing constraints considered in the first phase may be not preserved after the second one. In contrast, our work prioritizes preserving these constraints by directly designing the fully-connected HAD beamforming. We maximize the weighted sum rate while subject to power budget and radio-sensing constraints. To solve this, we propose an innovative iterative alternate optimization algorithm. Simulation results demonstrate performance close to that of a fully digital precoder, outperforming previous fully-connected hybrid beamforming methods for ISAC.