It is unlikely to support your weight
The weapon created by spiritual weapon is described as "spectral". There is no 5e definition of this word, but it is typically used for 'quasi-real' spell effects that can accomplish specific tasks but which in other ways are not physical objects. What these effects can do is enumerated in their spell description, but because they are spell effects and not objects we should assume they don't interact in the world in other ways beyond how they are said to.
Can a spectral force inhibit movement or be pushed against? For many effects the answer is no: Armor of Agathys makes armor, Mage Hand produces at most ten pounds of force, and the spectral shield produced by Wild Surge 51/52 interposes itself with attacks but doesn't stop things moving through its space.
Other spectral effects do interact with creatures in ways that can affect movement - the spectral vines produced by the Oath of the Ancient's Nature's Wrath can restrain a target, Spirit Guardians reduces creatures' speeds, and Guardian of Faith occupies its space the way a tangible object or creature might. Of all the spectral effects, the only one that might be able to bear weight is the Guardian of Faith. Because it occupies its space, presumably something landing on it from above or climbing onto it from below would be prevented from reaching the ground.
Since some spectral effects indicate that they can support weight (guardian of faith) while most don't, it is best to abide by the principle of 'spells do (only) what they say they do'. Spiritual weapon doesn't have any language that suggests that it exists physically or that it can be pushed off of, so it doesn't. You might be able to make a shield-sized disc as a weapon, but you wouldn't be able to stand on it - you would simply fall through the empty space.