A couple things to note:
In 5e, fInesse weapons can use strength or dex. I can't say I verified this, but I assume BG3 will apply the best for you.
In 5e it's really important to know what the strength based and dexterity based weapons are. If the wizard Evandir discussed above inadvertently decided to take proficiency in a longsword, rather than a rapier, it would be bad. The longsword is a strength based weapon, and the wizard probably has terrible strength, he would still get to add his proficiency bonus to the chance to hit, it would be nearly as good since his ability modifier would likely be 0, or even -1 or -2. He would have to stick to light or finesse to use his dex.
The proficiency for everything is the characters overall proficiency bonus, and will increase when we get to levels 5 (+3), 9 (+4) and, if the game goes that far, level 13 (+5). It tops out at +6 at level 17. Once they unlock level 5 everything you are proficient in will increase by +1; to hit, initiative, spell DC, spell attack, proficient saving throws...
I agree, I don't think you would typically want to give up an ability score increase to get weapon proficiency. The only builds I can see this might make sense are spellcasters if you want to focus on melee fighting and use your spells for healing and/or utility. For example, a Life Cleric might like to have heavy weapon proficiency if you want to do mostly melee damage and keep spells for healing and utility spells. In that build you can have a relatively low Wisdom (with low DC and spell attack modifier), pump up strength, and be effective in battle (at least in low levels.) Not how I would play it, but some might want to.
