When a copper pour area is poured, gaps are left around items that are on different nets from the copper itself. The size of these gaps is determined by the figures on the [Spacings] tab under Design Technology, exactly as if you were adding the copper interactively yourself.  The pour is always of type 'Shape' so it is these clearances which are used.

As well as the gaps between the copper and the items (determined by the Spacings), the linestyle width used for the Copper Pour area outline also determines the minimum pour width and hence where the Pour can 'reach' whilst obeying clearances.  In other words, making this outline thicker will require larger gaps between the pads for the copper to pour. Making it a smaller linestyle will mean it can pour into small 'gaps', and incidentally will also produce sharper corners, but you should be careful that the size is large enough for manufacture.