Yep, you are bumping the minimum spec for the software. It is odd that other vertex tools work easily and the Target Weld has issues. I'm guessing it's graphic card related. 

At any rate, here is the min. spec for 32bit Pentium rig (64bit has some major memory handling improvments if you need an excuse to get a new computer :-D )

32 bit

• Pentium 4 (or equivalent) or greater
• 1.3 GHz (2 GHz dual core or faster recommended)
• Windows 7, Vista, or XP
• 1 GB RAM min (2 GB+ recommended)
• 600 MB free hard drive space for installation
• Hardware accelerated OpenGL 1.3 compatible*(OpenGL 2.2, or higher, compatible recommended)*
• OpenGL 1.3 compatible graphics card with at least 128 MB RAM (Hardware accelerated OpenGL 2.2, or higher, compatible recommended with 512MB RAM)
• Drivers supporting OpenGL 1.3 or higher
• DirectX 9 (DirectX 10 recommended)