A boolean will in Console automatically show as a check box unless you enter in "True" and "False" text in the Properties of the Attribute in Object Designer. Doing this will make it show as a drop down list with the added values to select from. In Web Access the boolean will always show as a drop down list even though you haven't added in any "True" and "False" text.
To make a boolean show as a tick box in Web Access you will need to set the attribute to have a Default value of "False" and for it to be Mandatory. This is also done from Object Designer in the Properties of the Attribute.
After you have set this, do an IISReset and log back in and you should see the boolean being a check box and not a drop down list in Web Access.
The ability to change the 'Is Mandatory?' property on an attribute in Object Designer was introduced in 7.4. In versions prior to 7.4 the 'Is Mandatory?' property could only be set when you first created the object.