Scale doesn't connect with Wifi

That sounds frustrating.  I don't personally have an Index scale, but here are some possibilities.

What channel width for the Wi-Fi is set on the router?  The Garmin Index scale has been out for a few years, and some older devices won't connect successfully to the wider (above 20 MHz) channel widths.  I don't have a Garmin scale and thus can't say for sure that this is the cause, but it might be worth setting 20 MHz channel width to see what happens.

Also, some older devices don't connect successfully when the same SSID (the Wi-Fi network name) is configured for both the 2.4 GHz band and the 5 GHz band. If the router is configured with a single SSID for both bands then it might be worth reconfiguring so that the two bands have different SSIDs.

Further, some older devices don't correctly handle long, complex Wi-Fi network names and/or passwords -- those with characters in them that're not letters or numbers.  Spaces seem to trigger the issue most often.  At-signs ("@") are often problematic as well.

BTW, related to the channel-width,... It's generally considered best-practice to only use 20 MHz channels in the 2.4 GHz band (channels 1 - 14), using the wider channels only in the 5 GHz band (channels 36 and above.)  Also, the 2.4 GHz channel should be 1, 6, or 11. The numbering of 2.4 GHz channels is defined such that the frequencies used actually overlap, which causes interference and reduces performance.  Using 1, 6, and 11 only avoids the overlap.  The allocation of frequencies to channels in the 5 GHz band is more intuitive, so this overlap issue doesn't apply there.

-- Pete

P.S.  There's a forum specific to the Index scale under Sports & Fitness.  It might be appropriate to ask the moderators to move this post to that forum.