No such features are available. You can check size of the file after the conversion is completed but you cannot check the size of partially converted file during conversion. Aspose.Words supports an event to check the warnings during conversion and Aspose.Pdf supports checking the progress percentage during PDF to HTML conversion but no feature is available to check the size during conversion.
Adding more to Ijaz’s comments, if you are converting PDF file to TIFF format, you can specify TIFF compression using CompressionType enumerations. For further details, please visit Convert PDF pages to TIFF Image
In case you encounter any issue, please share the resource PDF file so that we can test the scenario at our end.