General synonyms:
* Make susceptible
* Make prone
* Make liable
* Make vulnerable
* Inclined
* Prone
* Susceptible
* Tendency
* Disposition
* Precipitate
More specific synonyms:
* Predetermine: (implies a strong influence that makes something almost inevitable)
* Influence: (suggests a less direct impact)
* Sensitize: (emphasizes heightened sensitivity to something)
* Prime: (implies preparation for a particular reaction)
* Condition: (implies a state of being that makes something more likely)
* Favor: (implies making something more likely to happen)
The best synonym will depend on the specific meaning you want to convey.