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In this paper a Weyl geometric scalar tensor theory of gravity with scalarfield $\Phi$ and scale invariant cubic ("aquadratic") kinetic Lagrangian isintroduced. Einstein gauge (comparable to Einstein frame in Jordan-Brans-Dicketheory) is most natural for studying trajectories. In it, the Weylian scaleconnection induces an additional acceleration which in the weak field, static,low velocity limit acquires the deep MOND form of Milgrom/Bekenstein's gravity.The energy momentum of $\Phi$ leads to another add on to Newton acceleration.Both additional accelerations together imply a MOND-ian phenomenology of themodel. It has unusual transition functions. They imply higher phantom energydensity than in the case of the more common MOND models with transitionfunctions $\mu_1(x), \, \mu_2(x)$. A considerable part of it is due to thescalar field's energy density which, in our model, gives a scale and generallycovariant expression for the self-energy of the gravitational field.

MOND-like acceleration in integrable Weyl geometric gravity