Fungal or bacterial rot is probably happening even with light watering, especially if humidity is high where you're keeping it. Jade plants are drought-tolerant but they're also susceptible to root rot when conditions stay damp - and here's the thing most people miss: even if your soil itself drains fast, if the pot sits in a saucer or tray that holds standing water, or if you're misting it occasionally, the leaves can stay wet long enough for pathogens to take hold. South-facing windows are great for light, but if that spot gets warm and humid (like from a humidifier nearby or just general summer moisture), it creates the perfect storm for fungal issues.
I'd cut back the watering immediately - maybe every three weeks or longer - and make sure you're not letting water sit under the pot. If the mushy parts are already extensive, you might need to repot into fresh, dry soil and pull away any soft or blackened roots. Jade plants bounce back pretty well once you stop the moisture problem, but you have to catch it before too much of the root system is compromised. If it keeps spreading even after you dial back the water, you're looking at needing to propagate healthy leaves and start fresh since the roots could be totally shot.