First of all, as pointed out in the question about moving areas of effect linked in Medix2's answer, there is some ambiguity as to whether spells like Spiritual Weapon can be controlled at all through any kind of total cover. Obviously, if the DM rules that they cannot, then Resilient Sphere completely prevents a creature inside the sphere from controlling their Spiritual Weapon outside it. So, that being said, for the remainder of this answer, let's assume your DM has ruled that existing movable spell effects are not limited by line of effect unless otherwise noted, so that, for example, you would be allowed to send your Spiritual Weapon over a 10-foot-high wall to attack someone on the other side even though the wall blocks direct line of effect from you to the target. With this in mind...
I would rule that an existing Spiritual Weapon continues functioning normally
Assuming, as described above, that line of effect is not an issue, nothing about the barrier of a Resilient Sphere spell prevents you from controlling an existing Spiritual Weapon through the barrier. The main problem is the final clause of the spell's 2nd paragraph (highlighted in bold):
Nothing–not physical objects, energy, or other spell effects–can pass through the barrier, in or out, though a creature in the sphere can breathe there. The sphere is immune to all damage, and a creature or object inside can't be damaged by attacks or effects originating from outside, nor can a creature inside the sphere damage anything outside it.
Taken alone, this clause clearly seems like it would prevent you from doing any damage with your Spiritual Weapon while trapped in the sphere. (Taking it ultra-literally, you could still attack and hit with it, but all the damage would be prevented.) However, consider that the entire paragraph is dedicated to describing the nature of the barrier and what can and cannot pass through it. Taken in context, I don't see any reason to read this final clause any more broadly than this: just like the rest of the paragraph, this clause only applies to effects that (try to) pass through the barrier. Reading the final clause of a 3-clause sentence as applying more generally than either of the other 2 clauses in the sentence or the remainder of the paragraph would not be a reasonable reading of a plain English sentence.
Hence, unless your DM rules that line of effect from the caster is required for re-targeting of ongoing spell effects, nothing in the Resilient Sphere spell prevents you from using your bonus action to attack and deal damage as normal with your Spiritual Weapon even while trapped inside the sphere. Similarly, a druid that had already cast Call Lightning before being trapped could continue using their action to call down lightning bolts on creatures outside the sphere, a cleric who had already cast Dawn could continue moving it as a bonus action and dealing damage with it, and so on.