It seems the OP asked this same question on another forum... so I'm going to answer the same way I did there:
It's Simply the Best Military Science-Fiction Series Ever. Period.
See, I got into the genre mostly thanks to Weber (I read HH 10 years ago for the first time). Usually, authors would have one or two things they like to write about. I could be space battles or infantry skirmishes or even political intrigue and subterfuge. HH has got it all. Pretty much everything you can think about: ship-to-ship, wall to wall, marines, pirates, asymmetrical warfare (aka terrorism), espionage, dogfights, hand-to-hand and even duels and swordfights. And all of this happening in the context of high stakes, larger than life heroes and dastardly villains but without overglorifying war (a lot of good guys dies, and not always in a nice way).
Another thing I like is how everything makes sense. There's some great worldbuilding, and not just when it comes to tech toys. Strategies and tactics are influenced by technological constraints, political circumstances, home cultures - just like in real life. People (or at least professionals) act base on what they know and the information they have at any given moment. Everything is consistent and there're not major plot holes as far as I can tell.
Now, I'm not going to claim it's flawless. Everything has a darker side. Weber is very detail oriented but sometimes infodumps can get too tedious. The later books are also verbose. It's not really politics per se (the scope becomes grander so it's inevitable). He has some kind of OCD in trying to relate the same events from different angles. So something happens and then you have a bunch of characters from each side (and there're like 10 interesting parties at this point) talking about it over and over again. And a lot of times it's not even the characters you care about. It adds up to a lot of filler.
I still read the last books because a) I'm already invested b) when it's good it's really good... I just wish DW got a good editor to trim the fat when necessary.
And I still think the first 8 or so books are the best in the genre and should be checked out by anyone looking for intelligent space opera.