Step 1. Weigh it. Kitchen scale says: .15 oz! No wait! .20 oz! No wait! .15oz ... So we record .175 oz. (Kitchen scale's "units" button is broken, so it gives oz and 20ths of an oz instead of grams.)
Step 2. Sink it. How can you measure volume precisely for a small object using only kitchen stuff? Measuring cup? Pah! Big wide surface, huge gradations. Is useless! Measuring spoon? Even worse! Wine bottle. Fill until there's water in the neck, Sharpie the meniscus, sink the thing, Sharpie the meniscus again.
Step 3. Measure. Tailor's tape, millimeters, 2.5mm between the tops of the Sharpie marks. Bottle inner diameter is maybe almost 19mm but it's hard to align both edges while maximizing... hm, what's the standard ID of a wine bottle? 18.5mm. OK, we'll go with that.
Step 4. Calculate. Google says: .175 oz / (2.5mm * pi * (18.5mm/2)^2) in g/cm^3 (typical units for specific gravity) ~= 7.4. Just right for bronze, a little light for brass or copper.
Step 5. Speculate. I'd say we have two significant figures, so we can consider heavy things like silver, lead, and gold ruled out, and light things like aluminium; but it's only a little bit high for tin or zinc, and very plausible for adding a bit of copper to those. Since there's a distinct coppery red where the surface is damaged, I'd lean toward calling it brass.
Further tests: stick it in lemon juice and see what it oxidizes and what it reduces?