2
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ListPointPlot3D[
 Table[Labeled[dataY[[i]], i], {i, 1, 
   Length[dataY]}], Filling -> Bottom, 
 AxesLabel -> {"O", "W", "C"}, 
 AspectRatio -> 1, ImageSize -> {500, 500}]

Is there a way to increase the size of the labelling of the points in the code above?

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4
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Apply Style[] to i:

ListPointPlot3D[
 Table[Labeled[dataY[[i]], Style[i,16]], {i, 1, 
   Length[dataY]}], Filling -> Bottom, 
 AxesLabel -> {"O", "W", "C"}, 
 AspectRatio -> 1, ImageSize -> {500, 500}]
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3
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You can also use the option LabelStyle. To keep the tick and axes labels unchanged add the option AxesStyle -> FontSize -> Medium:

dataY = RandomReal[10, {10, 3}];

ListPointPlot3D[Table[Labeled[dataY[[i]], i], {i, 1, Length[dataY]}], 
  LabelStyle -> Large, 
  AxesStyle -> FontSize -> Medium, 
  Filling -> Bottom, 
  AxesLabel -> {"O", "W", "C"}, 
  AspectRatio -> 1, ImageSize -> {500, 500}]

enter image description here

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