There are a few things that need to be addressed here. Sinus arrhythmia is a normal heart rhythm that varies with breathing; as you breathe in, your heart rate goes up. As you exhale, the heart rate goes down. This is not typically a problem. Interestingly, I was able to find an article about this online that does say that children with autism can have more wide-ranging heart rates associated with activity.
The other two conditions that you mention, tachy-brady syndrome and supraventricular tachycardia, are not normal conditions. Tachy-brady syndrome refers to abnormal function of the sinus node, the natural pacemaker of the heart. The heart rate speeds up easily, but also easily slows down too much in response to some medications. This can also happen if there is an atrial arrhythmia, such as atrial flutter or atrial fibrillation, which can abnormally remodel the sinus node. Sometimes patients require a pacemaker for this condition. If there is an atrial arrhythmia, an electrophysiology study with radiofrequency ablation can be performed. This is where the electrical system of the heart is fully evaluated, the site of the arrhythmia is found, and destroyed (ablated), thus eliminating the ability of the heart to go into the abnormal rhythm.
Supraventricular tachycardia (SVT) is an abnormal fast heart rhythm that occurs when there is an extra electrical connection between the top and the bottom of the heart. This allows an electrical impulse to go down the normal pathway and immediately back up the other one, allowing for a fast circular conduction circuit. As best as I can tell, this is not increased in children with autism. SVT can be treated with medications to prevent it or with an electrophysiology study with radiofrequency ablation.
The only other abnormality that I can find in the literature is a syndrome called Timothy syndrome, in which there is an abnormal calcium channel in the heart that leads to arrhythmias and also is associated with autism. I do not have enough information about your son to know whether this is something that he has, although there is genetic testing available for this at this time.
All of that said, based on the information that you have given me, I cannot find a cardiac reason that your son should be losing weight. Therefore, it would be appropriate to have a cardiologist further evaluate your son, and consider having an electrophysiologist, a cardiologist who specializes in the electrical system of the heart, evaluate him as well.