Weight gain, in general, is usually seen all over one's body, including the face. Just as we see many patients who have lost weight concerned with their facial appearance request dermal fillers, it stands to reason that weight gain may add some volume back to the face and may eliminate the desire to have dermal fillers. I would discuss any plans to intentionally gain weight for this reason with your doctor ahead of time to consider its effects on your overall health.
The risks of a Prothrombin mutation usually include a higher incidence of forming blood clots in blood vessels. This is not typically what we are most worried about when we are doing deeper injections of dermal fillers in a patient; we usually worry about conditions that thin the blood and lead to an increased risk of heavy bleeding. The most worrisome effect of having a prothrombin mutation is of having blood clots form in the larger deep veins of the legs or arms (DVT) or lungs (PE). That said, it's hard to predict whether your condition could predispose you to having complications of a local injection in your face, and potentially lead to blood clots forming in the smaller blood vessels causing the feared complication of skin breakdown, or necrosis. You're certainly right, that a non-dissolving filler such as Radiesse would be less safe than a hyaluronic based filler, which can potentially be dissolved with the enzyme, hyaluronidase. If a significant blood clot does form, however, it may not matter which filler was used. I would have a frank discussion with your doctor about the potential risks vs. benefits from using dermal fillers with your condition.
It's certainly possible to experience a droopy eyelid on one or both eyes after receiving Botox injections between the eyebrows for frown line treatments. This happens, rarely, when the Botox migrates from the injection site and has effects on an unintended muscle, in this case the one that lifts the eyelids. There is an eye drop that can be prescribed to try and lessen the eyelid heaviness experienced; ask your doctor about this as an option for you. Headaches can also occur after treatments with Botox, though usually would be expected to resolve after a few weeks. Continue to keep your doctor informed of your symptoms, however, as it is certainly possible your headaches are from another cause.
Until recently, this was a difficult area to treat, but newer products such as Belkyra (Canada), an injectable deoxycholic acid, can be used to dissolve the fat in targeted areas such as under the chin which bothers many people despite not being otherwise overweight.
This is a common question I receive, so you're not alone in having this fear. Most conservative injections of dermal fillers will not stretch the skin to any long-term degree. Your skin is an amazing organ which will adapt with time, so as the fillers begin to "dissolve", your skin will naturally tighten, especially if you're combining injectables with other treatments (skin care products, lasers, hydrafacials, Skin Pen, etc.) to maintain healthy and vibrant skin.