In-world, weapons tend to be described in terms of their unique features rather than numbers.
Other than "magic", "magical", "enchanted" or words of similar meaning, there is no strict in-world term for +1 or better weapons or items, nor for describing the exact gradiations of magical bonuses.
What you find, particularly in novels, is that characters almost never refer to their weapon in terms of its game statistics (plus one, plus two, etc), but rather in terms of how they perceive it. For example, take this section from the novel Cormyr:
Symylazarr, the Font of Honor, upon which the treacherous nobles had sworn fealty, was as broad as the Blade of Memory and etched along its blade with archaic runes. Orblyn, King Duar's mage-forged sword, with which he rallied the kingdom during the Pirate Exile, was a thinner, more modern blade. ...
Orblyn was covered with fine runes lightly etched into the blade. Salember had to hold the blade up to the light to see them clearly. The magical inscriptions seemed to twist and write as he watched. After all these years, Orblyn had held its edge and sharpness.
And later, when a magical weapon is used in battle:
The young prince reached the dragon and struck. His blade bit deep. The sword, supposedly crafted long ago by Amedahast herself, parted a scale as if it were jelly and slide into the creature's haunch, striking to the bone.
In The Two Swords, two magic weapons clash:
The greatsword burst into flame, but the startled Drizzt reacted perfectly, slapping Icingdeath across it.
The magic of the scimitar overruled the fires of the great-sword, extinguishing them in a puff of angry gray smoke, and it was Obould, suddenly, who was caught by surprise, just as he had started forward to overwhelm the drow.
Several other items in the same book are simply described as "enchanted", without reference to their precise power level. For example:
Drizzt motioned that he did not know. He pulled off his cloak, then loosened his enchanted, armored shirt so that he could pull one sleeve down over his hand.