Q:

Are Half-Elves supposed to have a slender build like Elves, or are they supposed to have a build that's intermediate between Humans and Elves?

The Player's Handbook's weight descriptions for Half-Elves are inconsistent.  The Half-Elf section in Chapter 2 (pg. 38) says:

They range from under 5 feet to about 6 feet tall, and from 100 to 180 pounds, with men only slightly taller and heavier than women.

However, the "Height and Weight Range" table in Chapter 4 (pg. 121) gives a weight formula for Half-Elves of 110 + (2d8) x (2d4), which is 114 to 238 pounds.
This is very different. 
Do we have any reason to label one description Correct and the other A Mistake?  The 2018 PHB Errata are silent on this point.
Looking at the rest of the table's formulas, Humans are 114 to 270 lbs, whereas Wood Elves are 102 to 180 lbs and High Elves are 92 to 170 lbs.  (I've excluded the Drow because they're significantly shorter.)
So are Half-Elves supposed to have a slender build like Elves (100-180 lbs), or are they supposed to have a build that's intermediate between Human and Elf (114-238 lbs)?
[As a side note, changing the Half-Elves' weight modifier in the table from its current 2d4 (which is like a Human's) to only 1d4 (like the Wood and High Elves') would yield a calculated range of 112 to 176 pounds.]
One possible avenue to explore:  I'm only familiar with 5e, but maybe one or more of the older versions of D&D can bring some clarity about the creators' intent.

A:

It's not a silly question, I'm also newish to this and have spotted similar discrepancies.
Earlier versions of DnD were much more specific. I have come to the conclusion that the authors of the new version have been deliberately vague on issues like this.
I can see a number of reasons for this-

Players can stick to their preconceptions 
Different miniature manufacturers have different takes on how characters are supposed to look
It reduces arguments on small details
It removes some of the maths

To answer your question more specially, it doesn’t matter what height and weight you put in, so build your character to your own preconceptions, the size data that has meaning is “Medium” the rest is just window dressing.
Hope this helps

A:

At least as early as 3e and 3.5e, Half-Elves have had a weight that is intermediate between Humans and Elves.
Human Weight (3e and 3.5e)
man: 120 + (2d10) x (2d4) lbs = 124 to 280 lbs
woman: 85 + (2d10) x (2d4) lbs = 89 to 245 lbs
Elf Weight (3e and 3.5e)
man: 85 + (2d6) x (1d6) lbs = 87 to 157 lbs
woman: 80 + (2d6) x (1d6) lbs = 82 to 152 lbs
Half-Elf Weight (3e and 3.5e)
man: 100 + (2d8) x (2d4) lbs = 104 to 228 lbs
woman: 80 + (2d8) x (2d4) lbs = 84 to 208 lbs

