I don’t think this is quite as simple as it’s being made out. I think you’re both going about this wrong, by not having a sensible adult discussion. You (and most PP) are assuming he’s after your inheritance, and he may be, but you don’t actually know that because you haven’t had an adult discussion about it.
Ultimately, you will have your two children living with you both most of the time, so it is right you contribute more to housing and other ongoing costs on that basis. You also have two children to his one. Again, you should be contributing more.
Exactly how much more is a matter for discussion - how did you come to the current agreed position regarding the deposit and what have you agreed for ongoing costs ? What was the basis in which you agreed it ?
Someone upthread mentioned a 60:40 split based on there being three in your family and two in his, but then is that fair if his child doesn’t get his own room and is barely there ? I wouldn’t think so if I was him. Looking at it like that I’d say maybe costs should be more like 75:25 split, as the DSS is there so infrequently with no space of his own he’s more like a visitor anyway, with this being reconsidered once the children move out or if there is a chance of circumstances (for example if your DSS moves in or stays more).
I know you say your DS will share also, but it will really be his room as he’s there most of the time, no matter how much you think (with a logical adult head) it won’t be. Kids don’t always feel like how you think they should and your DSS will feel more like a guest than he should. And what if he falls out with your DS ? Not having his own space will impact on how often he wants to visit his dad and could destroy that relationship.
You’ve also not mentioned the background much, but when I was younger I knew not a single person with shared bedrooms (although I acknowledge I was privileged). I think it depends what the children are used to.
There is no wrong or right answer, but this is why I do not understand why people want to “blend” families. It’s fraught with problems and worries. However, the more I think about it the more I think if you want to stick with a 3 bed you should be paying closer to 75% of the costs associated with it. If it’s to be a 4 bed, then more the 60:40 split with deposit / mortgage payments, but with a reduction in running costs for your DP as his son isn’t there much.
And any purchases should be done with legal advice to protect both your assets.
However, the fact the pair of you can’t seem to have a straightforward conversation about this and you questioning his motives leads me to think you shouldn’t be moving in together at all, or if you feel you must, then you should just rent to try it out first.