"Please give me a thick pen."
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I think it would generally be interpreted as the body of the pen itself is thick. When a pen has a bold tip, I see it labeled as 太字 (futoji, bold/thick characters), clarifying that the characters it writes are thick. The word for a pen tip/nib is ペン先, so ペン先が太い could also be used to specify that it is bold/thick-tipped pen.