When I weigh my keets I put an empty bowl on the scale and weigh it, then I put them in the bowl and subtracted the weight of the bowl. Or if that doesn't work I will use a wash cloth to loosely wrap them in and weigh them, then weigh the washcloth. It might not be 100% accurate but at least it is close. Also, I wouldn't necessarily put your budgie on a diet but instead worry about him getting the proper foods. Switch him over to pellets and start feeding him fresh vegetables and other healthy foods. Budgies have a very high metabolism and need to eat more than that a day. Also, if he is still only eating seed, even if it is for only 30 min. twice a day, he will still be unhealthy and not receiving any nutrition since seeds are basically fat. Budgies can be very stubborn about switching diets but if you stick with it, they will. It took mine 6 months to finally eat pellets. I would recommend getting small, unflavored pellets that resemble seeds. That is what I had the most luck with after trying 3 different kinds of pellets. Here is a link with some tips on getting birds to eat pellets.
Harrison's Bird Foods is a family of certified organic pet bird diets that were formulated to make your bird as healthy as it can possibly be.