Define in checkbox which string relates to checked value and which to unchecked value with the properties checkedValue
and uncheckedValue
:

<xp:checkBox
...
uncheckedValue="false"
checkedValue="true">
</xp:checkBox>
You can set the value then with
document1.replaceItemValue("picWeb", "true")
This is a complete example to demonstrate how to set a checkbox value in SSJS:
<?xml version="1.0" encoding="UTF-8"?>
<xp:view xmlns:xp="http://www.ibm.com/xsp/core">
<xp:this.data>
<xp:dominoDocument var="document1" formName="Test" />
</xp:this.data>
<xp:checkBox text="picWeb" id="checkBox1"
value="#{document1.picWeb}"
uncheckedValue="false"
checkedValue="true">
</xp:checkBox>
<xp:button value="True" id="button2">
<xp:eventHandler event="onclick" submit="false"
refreshMode="partial" refreshId="checkBox1">
<xp:this.action><![CDATA[#{javascript:
document1.replaceItemValue("picWeb", "true")
}]]></xp:this.action>
</xp:eventHandler>
</xp:button>
<xp:button value="False" id="button3">
<xp:eventHandler event="onclick" submit="false"
refreshMode="partial" refreshId="checkBox1">
<xp:this.action><![CDATA[#{javascript:
document1.replaceItemValue("picWeb", "false")
}]]></xp:this.action>
</xp:eventHandler>
</xp:button>
<xp:button value="Submit" id="button1">
<xp:eventHandler event="onclick" submit="true"
refreshMode="complete" immediate="false" save="true">
</xp:eventHandler>
</xp:button>
</xp:view>
The value is set in document as string
