Offset printing but only on labels

[JMC78]

I’m trying to print Avery labels using Avery’s own design software. The labels are offset each time I print. The offset is consistent across the page. Weirdly, the alignment is perfect on plain paper without changing any settings, but when label sheets are put through the printer the alignment inexplicably jumps about 2mm to the side and 1mm down. 
I’ve already set the scaling to 100% and tried setting the offset via Avery’s design software. 

[Dragon-Fur]

@JMC78 

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The problem, if there is one, is perhaps that this printer supports a limited range of media; most of these are "light weight".

What does "paper weight limitation" mean?

The limitation might be significant if (the weight of) your label paper exceeds the limits in the specifications for supported paper types. 

You cannot use "photo paper" - most printers do not let you select photo paper unless you actually load photo paper into the tray (sensors).

How heavy is your paper?

Hopefully, the weight of the paper is listed somewhere on the packaging.  This is sometimes the case.

References

 Printer Specifications for HP ENVY 5540, DeskJet 5570 Printers

and...

Media Size	Letter; A4; Legal; B5
Media Sizes Custom (imperial)	3.85 x 8.5 to 5 x 14 in
Media Sizes Custom (metric)	97.79 x 215 to 127 x 355 mm
Media Types	Paper (plain, inkjet, photo), envelopes, transparencies, labels, cards, the HP premium media, iron-on transfers, borderless media
Media Weight Recommended (imperial)	18 to 22 lb
Media Weight Recommended (metric)	70 to 90 g/m²
Media Weights Supported, By Paper Path (Imperial)	16 to 72 lb
Media Weights Supported, By Paper Path (metric)	Tray 1: A4: 75 to 90 g/m²; HP envelopes: 75 to 90 g/m²; HP Photo Paper: up to 250 g/m²; HP 10 x 15 cm photo paper: up to 250 g/m²

What else?

If the labels are "glossy",

If you do not have (find) an appropriate paper type in the list of papers,

The label paper might slip when grabbed and positioned for the job.

Lacking any control of the the paper type, there would be no actual "fix" for this.

Try / Consider

The following assumes that you have previously installed the Full Feature Software (full driver) for the printer.

Remove the paper from the main tray.

Count out six to ten sheets of label paper and load into the tray.

Load the paper into the printer according to the instructions in the User Guide

Starting on Page 10

Tell the Printer about the loaded paper and set the Preferences

Example

Retain_Printing_Preferences_1

Ope your Avery Project...

In the Design and Print software,

After you select the Print option, select to save the document to a PDF file.

Open the PDF file in Adobe Reader DC 

Set the print options on the main menu

Open Properties

Select shortcut "Everyday Printing" or similar

Look for a "heavier" paper type - Lacking Brochure matte / glossy, consider "Label" paper or "Card" paper

Set the paper size and the type of paper

Click OK to save the changes and edit the Properties menu

When ready, Print one copy of the label paper

Example - PDF - Avery Label

Avery_5200_Sample_Label_PDF_Print_1

Avery_J8161_Sample_Label_PDF_1

Will that work?

Maybe.

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When the website support page opens, Select (as available) a Category > Topic > Subtopic

HP ENVY 5546 All-in-One Printer 

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