What are some ways to measure sugar concentration of fruits?
The solute will alter the density of the solvent, which is used for example to determine the concentration of sulfuric acids by a hydrometer and in particular by help of a saccharometer.  Depending on your equipment you will need at least about 20 mL of analyte.
A popular alternative among winemakers is to rely on the change of the refractive index of a solution (refractometry) instead.  With portable devices as on the picture, you basically determine the critical angle of total reflection of the juice of few grapes placed on a prism.  The analysis is quick (seconds) and needs little (mL or less), the reading typically yields refractive index and content of sugars present as expressed for example in Oechsle, Baumé, Brix, or mass%.

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Note, however, that these techniques are not specific to sugar(s).  The presence of other compounds soluted equally may affect the refractive index, as well as the wavelength of light used and temperature during the recording.  To prevent adulteration of wine, for example, some more advanced refractometers already determine the refractive index at multiple wavelengths simultaneously, too.