You were right to take him to the vet to get that initial exam. By doing that you have ruled out most other common causes of weight loss.
When I took Blue to the vet I got a regular exam first and she recommended a dental exam. I did have statistics, though, about his weight that I kept in a spreadsheet and was able to demonstrate intense weight loss and acceleration in the trend and had a history to compare over several months. Although I didn't bore the vet with my chart and the gory details of it (which I posted to the forum) I was able to tell her what was happening and got the right test and a rapid diagnosis.
The fact is you don't have that same kind of information and there are still unknowns.
I am hoping for the best and that your pet does not have malocclusion or dental issues and I know you are worried about it. I became very obsessive towards the end when I was convinced my chin was sick but I also had hard evidence that he was. I am hoping that you will find that there is no decrease in weight and you still could find that to be the case.
This is what I do with my chinchillas. Perhaps someone else has some better ideas but my solution is the scientific approach.
Measure out the same amount of food your chinchilla every morning providing just slightly more pellets than he normally eats in a day but an generous amount of hay and weigh him every day although once a week should suffice. Record how much he eats and drinks. For my chin I just use a number between 1 and 5 for his food accounting for my best guess on his hay and pellets. I have a ruler strapped to my water bottle and I record how many centimeters it changes each day which is very precise. (remember to measure at the meniscus). I also record his weight when I get up in the morning and hold him up and look at his feet and just briefly examine him for anything out of the ordinary. I also have a notes section on my data sheet for recording abnormalities like the time I found his toe was lacerated, or if he had a bad experience with the baby who startled him the other the night, and that kind of thing. And if you write down things you're obsessing over (like little noises or sneezes or such) you can look back and you might just find they are normal little things.
If you weigh and measure every day it's easy to get obsessive over normal weight and food consumption fluctuations so avoid that temptation if you do and go by week to week figures. I find that my chinchilla can go up or down 10 grams sometimes but typically it's around 2.
When you have several weeks of data you can see what normal fluctuations look like and that makes it easier to spot abnormalities.
Personally I go over the top because I think plotting stuff is cool. I have a logging thermometer so I'll put the high and low room temp and humidity as well although my hygrometer is highly suspect.
Either way keep a data sheet with the numbers and compare. A veterinarian will be likely concerned if there is a decrease of 20% in weight that is not unexplainable, or if there is a sharp decrease in food or water intake. I think that a slightly underweight chinchilla that is otherwise healthy can probably stand to loose some more weight but the margin of safety will not be as good as if he started out at a healthy weight because there are so little fat reserves to fall back on. If you see a sharp trend like 2-4 grams per day for a week with no let up that should be pretty solid evidence before it gets to 20% or if he flat stops eating that is definitely an emergency.
So start logging and don't worry so much. It really is not worth it to worry over these things and to worry about loosing what we treasure. Nothing we have is owed to us nor is it permanent. It is always better to take life as it comes and make the best of whatever comes our way.