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Illithidbix on the subject of such weapons, if I were making stuff for 5e (and really any D&D game, but 5e in particular), I'd probably not hand out JUST +3 gear with no other attributes. Even in 4e, I don't think I'd do that--unless the party has a history of, or interest in, custom-tailoring their gear themselves. Instead, I'd have any weapon with a +3 (or higher) be something special, either a unique one-off creation or the result of some kind of profound magical event.
For 4e specifically, I'd also allow characters to layer their own enchantments on things (especially "quality of life" enchantments, e.g. the various enchantments that allow particular classes like Bard or Paladin to use them as implements). So whatever special properties they have would probably be either unique materials, or special custom-made features, more like a Boon attached to a specific item.
I'm actually quite keen on stuff like this, "unique"/"unusual" materials that "justify" the +1 or whatever. As an example of "+1 materials," I originally posted these elsewhere:
- Forgeboon. A "forgeboon" item results from an accidentally beneficial blending of multiple materials in a single alloy. Such mixes are notoriously difficult to produce intentionally, but lead to some blacksmiths intentionally leaving their smelters with traces of leftover metal to see what comes out. A "forgeboon" weapon may qualify as one or more material types for the purpose of hurting enemies which can only be harmed by specific substances--the DM should decide (or roll to decide) which. Forgeboon armor may possess the lightness of mithril or slight damage resistance of adamantium, the DM should decide (or roll to decide) what.
- Ravenglass. This is obsidian which formed under the influence of strong magical energy; perhaps a water elemental flash-freezing lava, or a Meteor Storm spell clashing with a Blizzard. Slashing and piercing ravenglass weapons have absurdly sharp edges and points, and have +1 to their critical threat range, which stacks with the Keen property and any other sources of increased threat range which are not stated to be exclusive. Crushing or blunt ravenglass weapons magically produce tiny slivers of glass; they gain Brutal 1 or increase their Brutal value by 1 if they already possess that property. Ravenglass armor retains some traces of the fire that was rapidly drained from it; any fire resistance the wearer possesses is increased by 5 for wearing it (as 'body-covering' armor).
- Witchfold. A "witchfolded" blade is one which has a simple, innate enchantment beaten into the metal itself. There are many closely-guarded, competing traditions. Actual practitioners of the arcane arts often find it difficult to produce witchfolded blades, so most are made by non-mages. One witchfolding style channels energy into the item, often from specially-selected reagents added to the forging fire and quenching vat, to create a primitive spirit or spirit-like entity which "lives" inside the blade. Edged weapons might have a "spirit of sharpness," making a blade that sharpens itself as it cuts. Blunt weapons might receive a spirit of "impact" or "thrust;" ranged weapons, a spirit of "swiftness"; for armor, a spirit of endurance, or a spirit of levity to lighten one's load. The DM may select (or roll to select) a single appropriate property for the item in question, though these properties should generally have little to no game effect (no more powerful than being unbreakable, or weighing half as much as usual, or the like).
Further (not-written-up) examples I gave were Unmelting Ice, Starmetal, or giant bones for +2 items. For very high-plus weapons (+3 in 5e, probably +5 or +6 in 4e) either items that are nearly impossible to find in nature, such as the bodily fluids of gods or shell fragments of dragons that are now ancient wyrms; or materials that have been exposed to magic for so long that they're now sources of magic in themselves, such as astral sandstone, oricalcum, or amber of the First Oak. Such things would be fantastically rare; finding them in sufficient quantity and quality to produce a useful item could be a fun quest in and of itself.