It seems awfully heavy at this age for a non english budgie, make sure you are not feeding too much at once as this can cause problems in the crop. Did you read the link I posted about hand feeding and weaning earlier in this thread?
Yes I have. I'm following that and I'm avoiding feeding more than 4 times a day if possible. He was 36 when I got him on the first day, so I guess he was fed that way by his mother or father. Who knows, maybe he is a quarter English budgie?
As long as you do not overfill the crop, you can feed him a little bit when he's hungry.
After having been without food for awhile when you first brought him home, he may be scared he isn't going to get more so he's letting you know he wants to eat when he first starts feeling hungry.
However, if he keeps gaining weight then you are going to need to cut back.
38 grams does seem to be high for a budgie his age.