If your goal is to have a thick (chestier) sound in your upper range, then bridging early isn’t going to get you there.
Bridging early will help balance your voice, and achieve good cord closure through your entire register. Bridging later will give you the advantage of more mouth and throat resonance with a tilted cartilage and narrowing of the aryepiglottic sphincter.
For example, I can sing high C with two different co-ordinations. One sound is more legit with great head resonance and cord closure. This is when I bridge around G above middle C. The second co-ordination is a thicker and chestier sound with stiffer cords. Because my thyroid is tilted and the AES tube is narrowed, the resonance doesn’t split the same as it does when bridging earlier. This gives the listener the impression of a thicker, chestier sound.