For what it's worth, the Guardian cites a comparison with a sportsperson (who unlike politicians seems less likely to have his height "doctored"):
One image showed Trump standing next to former baseball player Alex Rodriguez, who is 6ft 3in. Rodriguez looked considerably taller.
(There's a photo in the article, but it's copyrighted by Getty, and they are really touchy about non-authorized reproductions of their wares, so head over to the Guardian if you want to see it.)
The Guardian article also mentions that Trump's height on his driver license was 6'2" not 6'3". I'm not sure how correct that is either because when I've got a US driving license I simply declared my height, nobody measured it (they could have cross-checked against my passport, but they didn't.)
The Guardian also says:
A photo of Trump next to Barack Obama, taken one year ago at Trump’s inauguration, seemed to show that the pair were of the same height. Obama is 6ft 1in.
The Guardian article also talks about Trumps' weight in comparison to athletes of similar height but this probably even less relevant health-wise because differences in muscularity are apparent and thus so is the body fat percentage.
There's an AOL article which seem to clarify the 6'2" vs 6'3" as 6'2.5", and it also says that Trumps' physician suggested he lose some weight:
Standing at 75 inches tall, or 6' 2.5", and weighing in at 239 pounds, Trump's weight places him at a Body Mass Index (BMI) of 30.3, or, if his height is rounded up to 6' 3", 29.9.
Based on Trump's BMI, it is possible that he should consider losing 39 pounds, which would place him at a BMI of 25, right on the borderline of "normal weight" and "overweight" for someone of his height.
[discusses that BMI may be a poor measure of body fat]
Dr. Jackson said at Tuesday's briefing that after conducting last week's physical, he and the president set a goal of losing 10-15 pounds. If he kicks his notorious McDonald's habit, that target should be easily attainable.
Since weight varies a lot more than height over time in most people, I think it would much more difficult to confirm Trump's current weight...