Under Lifting and Carrying (PHB 176) it says:
Your carrying capacity is your Strength score multiplied by 15. This is the weight (in pounds) that you can carry…
You can push, drag, or lift a weight in pounds up to twice your carrying capacity (or 30 times your Strength score).
and also specifies that a tiny creature can carry half as much.
A sprite familiar summoned through a warlock's Pact of the Chain feature has a strength score of 3 and so has a carrying capacity of 22.5 pounds, and a push, drag, lift limit of 45 pounds. The sprite stat block also specifies, however, that they wear leather armor and carry a longsword and shortbow.
By the rules in the PHB, these weigh 10 pounds, 3 pounds, and 2 pounds respectively, but considering they are smaller than those worn by a medium humanoid it one should assume that they do not weigh as much.
Is there any official guidance as to how much the sprite familiar's equipment counts against its carrying capacity?
Best Answer
5e offers no guidance on the subject of equipment weight for differently sized creatures
Unlike previous editions, nowhere in 5e's published rules is the question of equipment weight for larger or smaller creatures addressed. The DMG's section on designing new monsters briefly addresses weapons sized for larger creatures:
But this is only about the damage the weapon deals. Weight is not addressed. As written, all equipment weighs the same no matter what size it is. This is obviously nonsense, but 5e's design has made a deliberate decision to elide these kind of concerns (in contrast to at least 3/3.5e, which covers the subject in a lot more detail). If the DM wants to get into this level of detail, they must decide for themselves what rulings to apply.
Personally, when I adjudicate item weight by creature size, I find that the easiest way to do it in the context of 5e's existing rules is simply to apply the same rules to equipment weight as apply to carrying capacity - which is to say, equipment for Tiny creatures weighs half what it normally does and equipment for creatures larger than Medium weighs double per step in size. It's not the most realistic ruling you could make, but it is at least consistent with the game's existing abstractions about weight and size.