You are confusing how <<continue>> works. You have to use <<break>> to stop the for loop from running:
<<for $count=0; $count <= $weapons_vet.length; $count++>>
<<if $weapons_vet[$count] is "empty">>
<<set $weapons_vet[$count] to "shotgun"; $weapons_damage[$cont] to 8; $weapon_equiped to $weapons_vet[$count]; $weapon_equipeddamage to $weapons_damage[$count]; $cont to $weapons_vet.length + 1>>
<<break>>
<<elseif $weapons_vet[$count] is "shotgun">>
<<print "You already have a shotgun.">>
<<break>>
<<endif>>
<<endfor>>
That being said - I don't know what you want to accomplish exactly, but this seems overly complicated. You can probably get the same result by using an empty array and a widget like this:
<<widget addWeapon>><<nobr>>
<<if $weapons.includes($args[0])>>
You already have a $args[0].
<<else>>
<<set $weapons.push($args[0])>>
<</if>>
<</nobr>><</widget>>
Then add weapons like this:
<<set $weapons to ["Gun", "Bomb", "Pointy Stick"]>>
<<addWeapon "Gun">>
<<addWeapon "Bear">>
$weapons