The explanation I was taught was that in strained ring structures, the hybridization of the carbon changes from sp to more p-like (because the geometry approaches 90 degrees). This means the C=O bond contains more s-character as the ring strain is increased, which strengthens/shortens the bond and leads to increased vibrational frequency.
To see if there were any alternative explanations, I first checked Silverstein and Webster (excellent resource, highly recommend to anyone interested in spectroscopic analysis of organic compounds). They put forward the following (p.94):
"In cyclic ketones, the bond angle of the C-(C=O)-C group influences the absorption frequency of the carbonyl group. The C=O stretching undoubtedly is affected by adjacent C-C stretching. In acyclic ketones and in ketones with a six membered ring, the angle is near 120 deg. In strained rings in which the angle is less than 120 deg., interction with the C-C bond stretching increases the energy required to produce C=O stretching and thus increases the stretching frequency. Cyclohexanone absorbs at 1715 cm-1, cyclopentanone absorbs at 1751 cm-1, and cyclobutanone absorbs at 1775 cm-1."
Not particularly informative, unfortunately. So I turned to the interweb and found this paper that might be of interest to you: Galabov and Simov, "The Stretching Vibration of Carbonyl Groups in Cyclic Ketones", Chem Phys Lett. 1970, 5(9), 549. https://www.researchgate.net/publication/244118717_The_stretching_vibration_of_carbonyl_groups_in_cyclic_ketones
They discuss the viability of the hybridization explanation as well as an alternative explanation: pure mechanical (kinetic energy) effects, which I interpret to mean that smaller rings physically restrict the amount of motion the various nuclei can possess. The paper concludes that both hybridization and mechanical effects contribute to the shifting vibrational frequencies, but in extremely small rings there must be additional effects at play.
These effects would be expected to influence the vibrational frequencies in other strained ring systems, including alkenes and alkanes. Obviously in lactones you also have the inductive effect of the adjacent oxygen to worry about.