Basically, it takes a long time to unlock weapons. Instead of just finding a weapon in the field and using it immediately, in Peace Walker (and subsequently MGSV) you find a weapon blueprint which then has to be developed by your R&D team back at Mother Base. At best, you'll be able to develop the weapon immediately, resulting in a wait timer of a certain length (a recent demo showed 18 minutes for a revolver). If you don't meet the requirements for the weapon's development, however, it means recruiting more dudes and leveling up your teams until you do. In Peace Walker, a weapon's development timer was progressed by completing missions, which meant grinding those suckers out by the dozen, and that game did not have enough content to warrant that much repetition.
The 'grindiness' varies from person to person, though. I've seen plenty of people here who feel Peace Walker wasn't grindy at all, whereas I personally felt that game was grind city. I feel that the huge amount of unique content in MGSV will make it feel much like much less of a grind, though, because you aren't going to be repeating the same levels over and over and over again in order to unlock things. Those gigantic levels are going to mean there's always somewhere you haven't explored, some mission you haven't done yet, so I imagine it'll be a much more pleasant experience this time around.