reckoner
No, and this is one of the few questions in training where the studies looked directly at what you are worried about.
Blagrove and colleagues reviewed 24 studies of strength training in middle and long distance runners. Running economy generally improved, and time trial performance and sprint qualities tended to improve too. The measures relating to body composition were not negatively affected by the strength training at all1.
Where the fear comes from
It is a reasonable fear and it is worth saying why. A runner carries their own body weight for the whole race, so anything that adds mass is a tax you pay every kilometer. And heavy lifting looks like the thing that makes people bigger, because for some people, doing something else, it is.
Why it does not happen to runners
What a runner is prescribed is not a program for adding size. In the review that sorted the training methods by what they actually were, the strength work that improved running performance was training at or above eighty per cent of a one repetition maximum, one to four sessions a week, over programs lasting from six to forty weeks2.
Heavy, few repetitions, not many sessions, sitting on top of a running volume that already costs a great deal of energy. That is a prescription for producing force, and across those studies it did that without the body composition measures moving against the runner1.
What changed and what did not
The thing that improved is running economy, which is the energy you spend holding a given pace. What was typically unaffected, across the same 24 studies, was maximal oxygen uptake, velocity at maximal oxygen uptake, blood lactate and body composition1.
So the honest version is narrow. Lifting is not a second way of training your engine and it is not a way of getting heavier either. It changes what a given pace costs you.
The caveat that belongs in the same breath
These are runners running a running program with lifting added to it. Somebody who lifts for size, eats for size and runs when they can is doing a different thing and will get a different result, and that result will include mass. If you have been told lifting made somebody slow, ask what else changed at the same time.
What Reckoner does
Reckoner writes each week from the sets you logged the week before, so the weight moves when your own reps say it should and holds when they say it should not. It is a strength coach and it does not see your running, so the mileage stays yours to plan. What it removes is the bookkeeping: knowing what heavy currently means on each of your lifts, week after week, as heavy keeps changing.