Does anyone have any ideas on upgrading a weapon to another tier. Some of my players have sentiment value in thier weapons and would not want to part with them

I'm not sure I follow.

Are you asking for ideas how to make a magical weapon get more powerful so the player doesn't feel hindered by continuing to use it for sentimental reasons? If so, my advice is this: don't ramp up the power of their weapon, and don't hand out more powerful weapons later - since magic items are already a bonus above and beyond what the system math expects of the character, the player will never feel like they are suffering from not moving on to a different weapon.

I meant to say, how could you turn a mundane weapon and give it +1. I guess like enchanting 

There are some magic item creation rules in the Dungeon Master's Guide, and a revised version in Xanathar's Guide to Everything (I prefer these revised rules).

I would just have them find a wizard and dish out some dough or complete a quest or something in order to have them "earn" it in some way. Which would be like your idea of enchanting.

I know this topic is dead for over a year, but why not create some quests that they have to go on to obtain materials for the upgrade that they can then take to a wizard, a cleric, a blacksmith, whoever you want and pay a fee plus the materials to upgrade their weapons? I really hate the system that's basically like "every time you want a better weapon either buy a new one or enchant it." You simply can't upgrade your current weapon to keep making it better? Really? I can't hand over dragon fangs I harvested off a beast I personally fought to forge on to a sword to add piercing or slicing damage? We can't get creative with this? Make your own system, I say.

Thank you, I appreciate the contribution. I've actually created a character in the group solely for that purpose. My group doesn't usually ask questions about the world, so this artificer acts as not only a an encyclopedia but a means to enchant items with materials he is brought.

this is just a suggestion,

I made a quest were there is a guy named Rio Magnus, he lives in the middle of the dead sea, and he has a map containing 6 artifacts. Rio wants you to bring them to him so he can create power to destroy a beholder. and since he is a scientist he can upgrade your weapons to help him destroy a beholder.

here is another example to upgrade weapons

sword > blue flame sword

great club > spiked great club

bow > spectre bow

hammer > bouncy hammer