I would read up on zoonoses! These are infectious diseases that, for a host of reasons, are able to make the leap from one species to another. Many of humankind's most terrible diseases are zoonoses: Ebola, flu, various poxes, plague, Zika, tuberculosis, many worms/parasites.
Zoonoses usually have a reservoir host species, in which the infectious organism causes little or no harm (avian influenza causes no illness in wild aquatic birds but if it makes the leap to us, can be deadly). The organism exists happily in this host, duplicating itself and carrying on until chance exposures lead to crossover events into a brand new species.
The Ebola outbreak in West Africa was hypothesized to have begun when a group of children played near a tree that was filled with Ebola-carrying bats and became infected. From the Ebola virus' perspective, it's not particularly useful to jump over to a human host that you are just going to kill off immediately- this does not promote the survival of the species! It was just a chance encounter that led to crossover- a matter of proximity and exposure.
Also, over time, killer viruses tend to become less potent in new hosts (HIV and some Ebola strains have done this)- this is a way of adapting and ensuring your host survives long enough to pass virus to lots of people. This evolution occurs once the organism has made the leap into humans and begins to adapt to the human immune system.
A cool example of virus evolution example is influenza, which has a variety of surface proteins that help the virus adhere to different mammalian species' cells with varying specificity. These proteins' genetic code "drift" and change over time naturally, leading to different strains of virus such as H1N1 or H3N2. If it ever shifts to a code that produces surface proteins that fit human respiratory cells receptors exactly (think like a lock and key), then we're looking at a pandemic event. Genetic change can happen faster when different virus strains recombine, like how swine flu was a mix of genes from human, avian, and pig-specific virus. Other animals like dogs are not susceptible to catching flu at all, because their receptors look totally different from ours/pigs/birds, which are all close enough to be shared around once in a while.
If you look up the life cycles of parasites like malaria or schistosomes, they often have complex relationships between different species in order to survive. Malaria has to, at different stages of its alien-esque life cycle, live in mosquitoes, humans, and the environment. Parasites can infect a ton of different species, which may or may not be the primary host, dead-end host, or reservoirs.
Anyway, you could certainly have a disease that halflings are immune to, or are reservoir hosts of, or can be infected by but only experience milder symptoms.