How much weight can a 3.5" deck screw hold before pulling out?
Deck screws are unsuitable for that use. They are light in gauge and usually have a bugle style head. You spaced them very close together so you are 'getting away with it' for now.
Most installations don't have a lot of direct pull out pressure, it's often mostly a shear load. Your installation is almost wholly in the pull out category.
In this situation I'd want a screw with flat bottomed head of a decent gauge (10 or 12 at least) and maybe even a washer to further resist pull out. You can increase the spacing but you'd still want at least 8 big screws. You can use a flat spade bit to drill small sockets or recesses to hide the screw head and washer.
There are various deck building framing screws which would be suitable, choose ones with large heads and thick gauges.