Is your unit allowed to give you a PT test and height/weight on the same day? I tried looking it up on 600-9, but I need a definite answer.

Every APFT I took was followed by a weigh in and measure, even the one I took at the SGM academy. Many do.

From AR 600-9 The Army Body Composition Program; para 3–4. Weigh-in and body fat assessment. b. In order to ensure the ABCP does not interfere with Soldier performance on the APFT, commanders and supervisors are encouraged to allow a minimum of 7 days between APFT and weigh-in, if feasible. Some Soldiers that are close to exceeding the screening weight may attempt to lose weight quickly in the days leading up to a weigh-in. This practice may result in the Soldier being unable to perform his or her best on the APFT, if the two events are scheduled close together.
App B–2. Height and weight measurements. b. The weight will be measured with the Soldier in stocking feet and wearing the authorized physical fitness uniform (trunks and T-shirt); running shoes will not be worn.
Note the "encouraged" and “if feasible” statements in the paragraph.

Is this for knowledge or because someone is worried about passing weight? Every Soldier in the US Army should be ready at anytime (barring recovery from a surgery or such) to be able to pass a PT test and HT/WT. If you are worried about being fat, because I have before, you need to step back and take a quick look at yourself and reasses were you are on stabdards

For the first 13 years of my career that's how it was done. Now in the last two years a lot of units have gone to doing them a week apart

That's how every unit I have ever been a part of does it. It's better for the Soldier as it gives you a chance to sweat off a few pounds.

It is not the preferred method, but it is authorized. It is actually outlined in both AR 350-1 and FM 7-22 where it talks about APFT and H/W. What is your issue with both being done on the same day?

Key word in the regulation is "encouraged" to allow seven days. I believe the max is 30 days and it was done due to Soldiers dropping dead on APFT's having cut too much water weight for the HT/WT. There are several regs for the APFT and HT/WT from the AR, FM, and TC.
All Soldiers are allowed to complain. However, losers complain with no solutions and winners fix the problem or find solutions. Be careful if looking to regs to prove your leaders wrong. Regs are black and white and most events in life and people are grey. You want a leader with experience and the regs to help guide, but if you wanted just the regs a robot could be your leader and that isn't how human interaction works.

It is not strictly forbidden so it is authorized to do so. It's not even pushing the limits to do so. If someone is so near to height weight that they need to "cut" in order to make it, they don't need to cut...they need to change their lifestyle.

Yes they may, although it is RECOMMENDED to do it no later than 7 days after the recorded APFT

It's not feasible for the Reserve components to do the two 7 days apart.

We have always done it the same day.